Link prediction for directed graphs is a crucial task with diverse real-world applications. Recent advances in embedding methods and Graph Neural Networks (GNNs) have shown promising improvements. However, these methods often lack a thorough analysis of their expressiveness and suffer from the lack of effective benchmarks for fair evaluation. In this paper, we propose a unified framework to assess the expressiveness of existing methods, highlighting the impact of dual embeddings and decoder design on directed link prediction performance. To address limitations in current benchmark setups, we introduce DirLinkBench, a robust new benchmark with comprehensive coverage, standardized evaluation, and modular extensibility. The results on DirLinkBench show that current methods struggle to achieve strong performance, while DiGAE outperforms other baselines overall. We further revisit DiGAE theoretically, showing its graph convolution aligns with GCN on an undirected bipartite graph. Inspired by these insights, we propose a novel Spectral Directed Graph Auto-Encoder SDGAE that achieves state-of-the-art average performance on DirLinkBench. Finally, we analyze key factors influencing directed link prediction and highlight open challenges in this field.

As the data demand for deep learning models increases, active learning (AL) becomes essential to strategically select samples for labeling, which maximizes data efficiency and reduces training costs. Real-world scenarios necessitate the consideration of incomplete data knowledge within AL. Prior works address handling out-of-distribution (OOD) data, while another research direction has focused on category discovery. However, a combined analysis of real-world considerations combining AL with OOD data and category discovery remains unexplored. To address this gap, we propose Joint Out-of-distribution filtering and data Discovery Active learning (Joda)1, to uniquely address both challenges simultaneously by filtering out OOD data before selecting candidates for labeling. In contrast to previous methods, we deeply entangle the training procedure with filter and selection to construct a common feature space that aligns known and novel categories while separating OOD samples. Unlike previous works, Joda is highly efficient and completely omits auxiliary models and training access to the unlabeled pool for filtering or selection. In extensive experiments on 18 configurations and 3 metrics, Joda consistently achieves the highest accuracy with the best class discovery to OOD filtering balance compared to state-of-the-art competitor approaches.

In panoptic segmentation, individual instances must be separated within semantic classes. As state-of-the-art methods rely on a pre-defined set of classes, they struggle with novel categories and out-of-distribution (OOD) data. This is particularly problematic in safety-critical applications, such as autonomous driving, where reliability in unseen scenarios is essential. We address the gap between outstanding benchmark performance and reliability by proposing Prior2Former (P2F), the first approach for segmentation vision transformers rooted in evidential learning. P2F extends the mask vision transformer architecture by incorporating a Beta prior for computing model uncertainty in pixel-wise binary mask assignments. This design enables high-quality uncertainty estimation that effectively detects novel and OOD objects enabling state-of-the-art anomaly instance segmentation and open-world panoptic segmentation. Unlike most segmentation models addressing unknown classes, P2F operates without access to OOD data samples or contrastive training on void (i.e., unlabeled) classes, making it highly applicable in real-world scenarios where such prior information is unavailable. Additionally, P2F can be flexibly applied to anomaly instance and panoptic segmentation. Through comprehensive experiments on the Cityscapes, COCO, SegmentMeIfYouCan, and OoDIS datasets, P2F demonstrates state-of-the-art performance across the board.

Many applications in traffic, civil engineering, or electrical engineering revolve around edge-level signals. Such signals can be categorized as inherently directed, for example, the water flow in a pipe network, and undirected, like the diameter of a pipe. Topological methods model edge signals with inherent direction by representing them relative to a so-called *orientation* assigned to each edge. They can neither model undirected edge signals nor distinguish if an edge itself is directed or undirected. We address these shortcomings by (i) revising the notion of *orientation equivariance* to enable edge direction-aware topological models, (ii) proposing *orientation invariance* as an additional requirement to describe signals without inherent direction, and (iii) developing EIGN, an architecture composed of novel direction-aware edge-level graph shift operators, that provably fulfils the aforementioned desiderata. It is the first work that discusses modeling directed and undirected signals while distinguishing between directed and undirected edges. A comprehensive evaluation shows that EIGN outperforms prior work in edge-level tasks, improving in RMSE on flow simulation tasks by up to 23.5%.

The accuracy of density functional theory hinges on the approximation of non-local contributions to the exchange-correlation (XC) functional. To date, machine-learned and human-designed approximations suffer from insufficient accuracy, limited scalability, or dependence on costly reference data. To address these issues, we introduce Equivariant Graph Exchange Correlation (EG-XC), a novel non-local XC functional based on equivariant graph neural networks (GNNs). Where previous works relied on semi-local functionals or fixed-size descriptors of the density, we compress the electron density into an SO(3)-equivariant nuclei-centered point cloud for efficient non-local atomic-range interactions. By applying an equivariant GNN on this point cloud, we capture molecular-range interactions in a scalable and accurate manner. To train EG-XC, we differentiate through a self-consistent field solver requiring only energy targets. In our empirical evaluation, we find EG-XC to accurately reconstruct `gold-standard' CCSD(T) energies on MD17. On out-of-distribution conformations of 3BPA, EG-XC reduces the relative MAE by 35% to 50%. Remarkably, EG-XC excels in data efficiency and molecular size extrapolation on QM9, matching force fields trained on 5 times more and larger molecules. On identical training sets, EG-XC yields on average 51% lower MAEs.

Recent advances in machine learning for molecules exhibit great potential for facilitating drug discovery from in silico predictions. Most models for molecule generation rely on the decomposition of molecules into frequently occurring substructures (motifs), from which they generate novel compounds. While motif representations greatly aid in learning molecular distributions, such methods fail to represent substructures beyond their known motif set, posing a fundamental limitation for discovering novel compounds. To address this limitation and enhance structural expressivity, we propose to separate structure from features by abstracting motifs to scaffolds and, subsequently, allocating atom and bond types. To this end, we introduce a novel factorisation of the molecules' data distribution that considers the entire molecular context and facilitates learning adequate assignments of atoms and bonds to scaffolds. Complementary to this, we propose MAGNet, the first model to freely learn motifs. Importantly, we demonstrate that MAGNet's improved expressivity leads to molecules with more structural diversity and, at the same time, diverse atom and bond assignments.

We introduce a new framework for 2D molecular graph generation using 3D molecule generative models. Our Synthetic Coordinate Embedding (SyCo) framework maps 2D molecular graphs to 3D Euclidean point clouds via synthetic coordinates and learns the inverse map using an E($n$)-Equivariant Graph Neural Network (EGNN). The induced point cloud-structured latent space is well-suited to apply existing 3D molecule generative models. This approach simplifies the graph generation problem into a point cloud generation problem followed by node and edge classification tasks, without relying on molecular fragments nor autoregressive decoding. Further, we propose a novel similarity-constrained optimization scheme for 3D diffusion models based on inpainting and guidance. As a concrete implementation of our framework, we develop EDM-SyCo based on the E(3) Equivariant Diffusion Model (EDM). EDM-SyCo achieves state-of-the-art performance in distribution learning of molecular graphs, outperforming the best non-autoregressive methods by more than 26\% on ZINC250K and 16\% on the GuacaMol dataset while improving conditional generation by up to 3.9 times.

Recent advancements in generative modeling, particularly diffusion models, have opened new directions for time series modeling, achieving state-of-the-art performance in forecasting and synthesis. However, the reliance of diffusion-based models on a simple, fixed prior complicates the generative process since the data and prior distributions differ significantly. We introduce TSFlow, a conditional flow matching (CFM) model for time series combining Gaussian processes, optimal transport paths, and data-dependent prior distributions. By incorporating (conditional) Gaussian processes, TSFlow aligns the prior distribution more closely with the temporal structure of the data, enhancing both unconditional and conditional generation. Furthermore, we propose conditional prior sampling to enable probabilistic forecasting with an unconditionally trained model. In our experimental evaluation on eight real-world datasets, we demonstrate the generative capabilities of TSFlow, producing high-quality unconditional samples. Finally, we show that both conditionally and unconditionally trained models achieve competitive results across multiple forecasting benchmarks.

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning models for point processes are predominantly constrained by their reliance on the characteristic intensity function, introducing an inherent trade-off between efficiency and flexibility. In this paper, we introduce Point Set Diffusion, a diffusion-based latent variable model that can represent arbitrary point processes on general metric spaces without relying on the intensity function. By directly learning to stochastically interpolate between noise and data point sets, our approach effectively captures the distribution of point processes and enables efficient, parallel sampling and flexible generation for complex conditional tasks. Experiments on synthetic and real-world datasets demonstrate that Point Set Diffusion achieves state-of-the-art performance in unconditional and conditional generation of spatial and spatiotemporal point processes while providing up to orders of magnitude faster sampling.

Machine learning models are highly vulnerable to label flipping, i.e., the adversarial modification (poisoning) of training labels to compromise performance. Thus, deriving robustness certificates is important to guarantee that test predictions remain unaffected and to understand worst-case robustness behavior. However, for Graph Neural Networks (GNNs), the problem of certifying label flipping has so far been unsolved. We change this by introducing an exact certification method, deriving both sample-wise and collective certificates. Our method leverages the Neural Tangent Kernel (NTK) to capture the training dynamics of wide networks enabling us to reformulate the bilevel optimization problem representing label flipping into a Mixed-Integer Linear Program (MILP). We apply our method to certify a broad range of GNN architectures in node classification tasks. Thereby, concerning the worst-case robustness to label flipping: $(i)$ we establish hierarchies of GNNs on different benchmark graphs; $(ii)$ quantify the effect of architectural choices such as activations, depth and skip-connections; and surprisingly, $(iii)$ uncover a novel phenomenon of the robustness plateauing for intermediate perturbation budgets across all investigated datasets and architectures. While we focus on GNNs, our certificates are applicable to sufficiently wide NNs in general through their NTK. Thus, our work presents the first exact certificate to a poisoning attack ever derived for neural networks, which could be of independent interest. The code is available at https://github.com/saper0/qpcert.

Conformal prediction provides model-agnostic and distribution-free uncertainty quantification through prediction sets that are guaranteed to include the ground truth with any user-specified probability. Yet, conformal prediction is not reliable under poisoning attacks where adversaries manipulate both training and calibration data, which can significantly alter prediction sets in practice. As a solution, we propose reliable prediction sets (RPS): the first efficient method for constructing conformal prediction sets with provable reliability guarantees under poisoning. To ensure reliability under training poisoning, we introduce smoothed score functions that reliably aggregate predictions of classifiers trained on distinct partitions of the training data. To ensure reliability under calibration poisoning, we construct multiple prediction sets, each calibrated on distinct subsets of the calibration data. We then aggregate them into a majority prediction set, which includes a class only if it appears in a majority of the individual sets. Both proposed aggregations mitigate the influence of datapoints in the training and calibration data on the final prediction set. We experimentally validate our approach on image classification tasks, achieving strong reliability while maintaining utility and preserving coverage on clean data. Overall, our approach represents an important step towards more trustworthy uncertainty quantification in the presence of data poisoning.

Comprehensive evaluation of Large Language Models (LLMs) is an open research problem. Existing evaluations rely on deterministic point estimates generated via greedy decoding. However, we find that deterministic evaluations fail to capture the whole output distribution of a model, yielding inaccurate estimations of model capabilities. This is particularly problematic in critical contexts such as unlearning and alignment, where precise model evaluations are crucial. To remedy this, we introduce the first formal probabilistic evaluation framework for LLMs. Namely, we propose novel metrics with high probability guarantees concerning the output distribution of a model. Our metrics are application-independent and allow practitioners to make more reliable estimates about model capabilities before deployment. Our experimental analysis reveals that deterministic evaluations falsely indicate successful unlearning and alignment, whereas our probabilistic evaluations better capture model capabilities. We show how to overcome challenges associated with probabilistic outputs in a case study on unlearning by introducing (1) a novel loss based on entropy optimization, and (2) adaptive temperature scaling. We demonstrate that our approach significantly enhances unlearning in probabilistic settings on recent benchmarks. Overall, our proposed shift from point estimates to probabilistic evaluations of output distributions represents an important step toward comprehensive evaluations of LLMs.

While uncertainty estimation for graphs recently gained traction, most methods rely on homophily and deteriorate in heterophilic settings. We address this by analyzing message passing neural networks from an information-theoretic perspective and developing a suitable analog to data processing inequality to quantify information throughout the model’s layers. In contrast to non-graph domains, information about the node-level prediction target can increase with model depth if a node’s features are semantically different from its neighbors. Therefore, on heterophilic graphs, the latent embeddings of an MPNN each provide different information about the data distribution - different from homophilic settings. This reveals that considering all node representations simultaneously is a key design principle for epistemic uncertainty estimation on graphs beyond homophily. We empirically confirm this with a simple post-hoc density estimator on the joint node embedding space that provides state-of-the-art uncertainty on heterophilic graphs. At the same time, it matches prior work on homophilic graphs without explicitly exploiting homophily through post-processing.

To circumvent the alignment of large language models (LLMs), current optimization-based adversarial attacks usually craft adversarial prompts by maximizing the likelihood of a so-called affirmative response. An affirmative response is a manually designed start of a harmful answer to an inappropriate request. While it is often easy to craft prompts that yield a substantial likelihood for the affirmative response, the attacked model frequently does not complete the response in a harmful manner. Moreover, the affirmative objective is usually not adapted to model-specific preferences and essentially ignores the fact that LLMs output a distribution over responses. If low attack success under such an objective is taken as a measure of robustness, the true robustness might be grossly overestimated. To alleviate these flaws, we propose an adaptive and semantic optimization problem over the population of responses. We derive a generally applicable objective via the REINFORCE policy-gradient formalism and demonstrate its efficacy with the state-of-the-art jailbreak algorithms Greedy Coordinate Gradient (GCG) and Projected Gradient Descent (PGD). For example, our objective doubles the attack success rate (ASR) on Llama3 and increases the ASR from 2% to 50% with circuit breaker defense.

Despite recent advances in subquadratic attention mechanisms or state-space models, processing long token sequences still imposes significant computational requirements. Token merging has emerged as a solution to increase computational efficiency in computer vision architectures. In this work, we perform the first investigations of token merging in time series analysis on both transformers and state-space models. We further introduce local merging, a domain-specific token merging algorithm that selectively combines tokens within a local neighborhood, achieving two major benefits: a) Local merging can adjust its computational complexity from quadratic to linear based on the neighborhood size to effectively scale to long sequences; b) Local merging is the first causal merging scheme enabling token merging in transformer decoders. Further, we identify spectral properties of the input data that reliably predict the potential benefits of local merging without requiring evaluation on downstream tasks. Our comprehensive empirical evaluation demonstrates that local merging offers substantial efficiency gains with minimal impact on accuracy, achieving up to 5400% acceleration on the recently proposed Chronos foundation model.

State space models are emerging as a dominant model class for sequence problems with many relying on the HiPPO framework to initialize their dynamics. However, HiPPO fundamentally assumes data to be noise-free; an assumption often violated in practice. We extend the HiPPO theory with measurement noise and derive an uncertainty-aware initialization for state space model dynamics. In our analysis, we interpret HiPPO as a linear stochastic control problem where the data enters as a noise-free control signal. We then reformulate the problem so that the data become noisy outputs of a latent system and arrive at an alternative dynamics initialization that infers the posterior of this latent system from the data without increasing runtime. Our experiments show that our initialization improves the resistance of state-space models to noise both at training and inference time.

Latent space interpolations are a powerful tool for navigating deep generative models in applied settings. An example is single-cell RNA sequencing, where existing methods model cellular state transitions as latent space interpolations with variational autoencoders, often assuming linear shifts and Euclidean geometry. However, unless explicitly enforced, linear interpolations in the latent space may not correspond to geodesic paths on the data manifold, limiting methods that assume Euclidean geometry in the data representations. We introduce FlatVI, a novel training framework that regularises the latent manifold of discrete-likelihood variational autoencoders towards Euclidean geometry, specifically tailored for modelling single-cell count data. By encouraging straight lines in the latent space to approximate geodesic interpolations on the decoded single-cell manifold, FlatVI enhances compatibility with downstream approaches that assume Euclidean latent geometry. Experiments on synthetic data support the theoretical soundness of our approach, while applications to time-resolved single-cell RNA sequencing data demonstrate improved trajectory reconstruction and manifold interpolation.

Many forms of sensitive data, such as web traffic, mobility data, or hospital occupancy, are inherently sequential. The standard method for training machine learning models while ensuring privacy for units of sensitive information, such as individual hospital visits, is differentially private stochastic gradient descent (DP-SGD). However, we observe in this work that the formal guarantees of DP-SGD are incompatible with time series specific tasks like forecasting, since they rely on the *privacy amplification* attained by training on small, unstructured batches sampled from an unstructured dataset. In contrast, batches for forecasting are generated by (1) sampling sequentially structured time series from a dataset, (2) sampling contiguous subsequences from these series, and (3) partitioning them into context and ground-truth forecast windows. We theoretically analyze the privacy amplification attained by this *structured subsampling* to enable the training of forecasting models with sound and tight event- and user-level privacy guarantees. Towards more private models, we additionally prove how data augmentation amplifies privacy in self-supervised training of sequence models. Our empirical evaluation demonstrates that amplification by structured subsampling enables the training of forecasting models with strong formal privacy guarantees.

The safety alignment of large language models (LLMs) can be circumvented through adversarially crafted inputs, yet the mechanisms by which these attacks bypass safety barriers remain poorly understood. Prior work suggests that a *single* refusal direction in the model's activation space determines whether an LLM refuses a request. In this study, we propose a novel gradient-based approach to representation engineering and use it to identify refusal directions. Contrary to prior work, we uncover multiple independent directions and even multi-dimensional *concept cones* that mediate refusal. Moreover, we show that orthogonality alone does not imply independence under intervention, motivating the notion of *representational independence* that accounts for both linear and non-linear effects. Using this framework, we identify mechanistically independent refusal directions. We show that refusal mechanisms in LLMs are governed by complex spatial structures and identify functionally independent directions, confirming that multiple distinct mechanisms drive refusal behavior. Our gradient-based approach uncovers these mechanisms and can further serve as a foundation for future work on understanding LLMs.

Expressivity theory, characterizing which graphs a GNN can distinguish, has become the predominant framework for analyzing GNNs, with new models striving for higher expressivity. However, we argue that this focus is misguided: First, higher expressivity is not necessary for most real-world tasks as these tasks rarely require expressivity beyond the basic WL test. Second, expressivity theory's binary characterization and idealized assumptions fail to reflect GNNs' practical capabilities. To overcome these limitations, we propose Message Passing Complexity (MPC): a continuous measure that quantifies the difficulty for a GNN architecture to solve a given task through message passing. MPC captures practical limitations like over-squashing while preserving the theoretical impossibility results from expressivity theory, effectively narrowing the gap between theory and practice. Through extensive validation on fundamental GNN tasks, we show that MPC's theoretical predictions correlate with empirical performance, successfully explaining architectural successes and failures. Thereby, MPC advances beyond expressivity theory to provide a more powerful framework for understanding and developing GNN architectures.

Building generative models for relational databases (RDBs) is important for many applications, such as privacy-preserving data release and augmenting real datasets. However, most prior works either focus on single-table generation or adapt single-table models to the multi-table setting by relying on autoregressive factorizations and sequential generation. These approaches limit parallelism, restrict flexibility in downstream applications, and compound errors due to commonly made conditional independence assumptions. In this paper, we propose a fundamentally different approach: jointly modeling all tables in an RDB without imposing any table order. By using a natural graph representation of RDBs, we propose the Graph-Conditional Relational Diffusion Model (GRDM), which leverages a graph neural network to jointly denoise row attributes and capture complex inter-table dependencies. Extensive experiments on six real-world RDBs demonstrate that our approach substantially outperforms autoregressive baselines in modeling multi-hop inter-table correlations and achieves state-of-the-art performance on single-table fidelity metrics. Our code is available at https://github.com/ketatam/rdb-diffusion.

In this work, we introduce TreeGen, a novel generative framework modeling distributions over hierarchies. We extend Bayesian Flow Networks (BFNs) to enable transitions between probabilistic and discrete hierarchies parametrized via categorical distributions. Our proposed scheduler provides smooth and consistent entropy decay across varying numbers of categories. We empirically evaluate TreeGen on the jet-clustering task in high-energy physics, demonstrating that it consistently generates valid trees that adhere to physical constraints and closely align with ground-truth log-likelihoods. Finally, by comparing TreeGen’s samples to the exact posterior distribution and performing likelihood maximization via rejection sampling, we demonstrate that TreeGen outperforms various baselines.

In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular systems. However, while classical diffusion sampling usually recovers the training distribution, the corresponding energy-based interpretation of the learned score is often inconsistent with this distribution, even for low-dimensional toy systems. We trace this inconsistency to inaccuracies of the learned score at very small diffusion timesteps, where the model must capture the correct evolution of the data distribution. In this regime, diffusion models fail to satisfy the Fokker-Planck equation, which governs the evolution of the score. We interpret this deviation as one source of the observed inconsistencies and propose an energy-based diffusion model with a Fokker-Planck-derived regularization term to enforce consistency. We demonstrate our approach by sampling and simulating multiple biomolecular systems, including fast-folding proteins, and by introducing a state-of-the-art transferable Boltzmann emulator for dipeptides that supports simulation and achieves improved consistency and efficient sampling. Our code, model weights, and self-contained JAX and PyTorch notebooks are available at https://github.com/noegroup/ScoreMD.

Understanding the evolution of cellular microenvironments in spatiotemporal data is essential for deciphering tissue development and disease progression. While experimental techniques like spatial transcriptomics now enable high-resolution mapping of tissue organization across space and time, current methods that model cellular evolution operate at the single-cell level, overlooking the coordinated development of cellular states in a tissue. We introduce NicheFlow, a flow-based generative model that infers the temporal trajectory of cellular microenvironments across sequential spatial slides. By representing local cell neighborhoods as point clouds, NicheFlow jointly models the evolution of cell states and spatial coordinates using optimal transport and Variational Flow Matching. Our approach successfully recovers both global spatial architecture and local microenvironment composition across diverse spatiotemporal datasets, from embryonic to brain development.

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Abstract Knowledge transfer is an effective method for learning, particularly useful when labeled data are limited or when training a model from scratch is too expensive. Most of the research on transfer learning focuses on achieving accurate models, overlooking the crucial aspect of adversarial robustness. However, ensuring robustness is vital, especially when applying transfer learning in safety-critical domains. We compare robustness of models obtained by 11 training procedures on source domains and 3 retraining schemes on target domains, including normal, adversarial, contrastive, and Lipschitz constrained training variants. Robustness is analyzed by adversarial attacks with respect to two different transfer learning model outputs: (i) the latent representations and (ii) the predictions. Studying latent representations in correlation with predictions is crucial for robustness of transfer learning models, since they are solely learned on the source domain. Besides adversarial attacks that aim at changing the prediction, we also analyze the effect of directly attacking representations. Our results show that adversarial robustness can transfer across domains, but effective robust transfer learning requires techniques that ensure robustness independent of the training data to preserve them during the transfer. Retraining on the target domain has a minor impact on the robustness of the target model. Representations exhibit greater robustness compared to predictions across both the source and target domain.

Recent advances in Artificial Intelligence have enabled multi-modal systems to model and translate diverse information spaces. Extending beyond text and vision, we introduce OneProt, a multi-modal Deep Learning model for proteins that integrates structural, sequence, text, and binding site data. Using the ImageBind framework, OneProt aligns the latent spaces of protein modality encoders in a lightweight fine-tuning scheme that focuses on pairwise alignment with sequence data, rather than requiring full matches. This novel approach comprises a mix of Graph Neural Networks and transformer architectures. It demonstrates good performance in retrieval tasks and showcases the efficacy of multi-modal systems in Protein Machine Learning through a broad spectrum of downstream baselines, including enzyme function prediction and binding site analysis. Furthermore, OneProt enables the transfer of representational information from specialized encoders to the sequence encoder, enhancing capabilities for distinguishing evolutionarily related and unrelated sequences and exhibiting representational properties where evolutionarily related proteins align in similar directions within the latent space. In addition, we extensively investigate modality ablations to identify the encoders that contribute the most to predictive performance, highlighting the significance of the binding site encoder, which has not been used in similar models previously. This work expands the horizons of multi-modal protein models, paving the way for transformative applications in drug discovery, biocatalytic reaction planning, and protein engineering.

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned, autoregressive models. However, the intricacies of turbulence in three dimensions necessitate training these models with very small time steps, while generating realistic flow states requires either long roll-outs with many steps and significant error accumulation or starting from a known, realistic flow state—something we aimed to avoid in the first place. Instead, we propose to approach turbulent flow simulation as a generative task directly learning the manifold of all possible turbulent flow states without relying on any initial flow state. For our experiments, we introduce a challenging 3D turbulence dataset of high-resolution flows and detailed vortex structures caused by various objects and derive two novel sample evaluation metrics for turbulent flows. On this dataset, we show that our generative model captures the distribution of turbulent flows caused by unseen objects and generates high-quality, realistic samples amenable for downstream applications without access to any initial state.

Uncertainty Sampling is an Active Learning strategy that aims to improve the data efficiency of machine learning models by iteratively acquiring labels of data points with the highest uncertainty. While it has proven effective for independent data its applicability to graphs remains under-explored. We propose the first extensive study of Uncertainty Sampling for node classification: (1) We benchmark Uncertainty Sampling beyond predictive uncertainty and highlight a significant performance gap to other Active Learning strategies. (2) We develop ground-truth Bayesian uncertainty estimates in terms of the data generating process and prove their effectiveness in guiding Uncertainty Sampling toward optimal queries. We confirm our results on synthetic data and design an approximate approach that consistently outperforms other uncertainty estimators on real datasets. (3) Based on this analysis, we relate pitfalls in modeling uncertainty to existing methods. Our analysis enables and informs the development of principled uncertainty estimation on graphs.

Although recent advances in higher-order Graph Neural Networks (GNNs) improve the theoretical expressiveness and molecular property predictive performance, they often fall short of the empirical performance of models that explicitly use fragment information as inductive bias. However, for these approaches, there exists no theoretic expressivity study. In this work, we propose the Fragment-WL test, an extension to the well-known Weisfeiler & Leman (WL) test, which enables the theoretic analysis of these fragment-biased GNNs. Building on the insights gained from the Fragment-WL test, we develop a new GNN architecture and a fragmentation with infinite vocabulary that significantly boosts expressiveness. We show the effectiveness of our model on synthetic and real-world data where we outperform all GNNs on Peptides and have $12$% lower error than all GNNs on ZINC and $34$% lower error than other fragment-biased models. Furthermore, we show that our model exhibits superior generalization capabilities compared to the latest transformer-based architectures, positioning it as a robust solution for a range of molecular modeling tasks.

In mobile robotics, particularly in autonomous driving, localization is one of the key challenges for navigation and planning. For safe operation in the open world where vulnerable participants are present, precise and guaranteed safe localization is required. While current classical fusion approaches are safe due to provably bounded closed-form formulation, their situation-adaptivity is limited. In contrast, data-driven approaches are situation-adaptive based on the underlying training data but unbounded and unsafe. In our work, we propose a novel data-driven but provably bounded sensor fusion and apply it to mobile robotic localization. In extensive experiments using an autonomous driving test vehicle, we show that our fusion method outperforms other safe fusion approaches.

Effectively designing molecular geometries is essential to advancing pharmaceutical innovations, a domain, which has experienced great attention through the success of generative models and, in particular, diffusion models. However, current molecular diffusion models are tailored towards a specific downstream task and lack adaptability. We introduce UniGuide, a framework for controlled geometric guidance of unconditional diffusion models that allows flexible conditioning during inference without the requirement of extra training or networks. We show how applications such as structure-based, fragment-based, and ligand-based drug design are formulated in the UniGuide framework and demonstrate on-par or superior performance compared to specialised models. Offering a more versatile approach, UniGuide has the potential to streamline the development of molecular generative models, allowing them to be readily used in diverse application scenarios.

Neural network sparsification is a promising avenue to save computational time and memory costs, especially in an age where many successful AI models are becoming too large to naively deploy on consumer hardware. While much work has focused on different weight pruning criteria, the overall sparsifiability of the network, i.e., its capacity to be pruned without quality loss, has often been overlooked. We present Sparsifiability via the Marginal likelihood (SpaM), a sparsification framework that highlights the effectiveness of using the Bayesian marginal likelihood in conjunction with sparsity-inducing priors for making neural networks more sparsifiable. Our approach implements an automatic Occam's razor that selects the most sparsifiable model that still explains the data well, both for structured and unstructured sparsification. In addition, we demonstrate that the pre-computed posterior precision from the Laplace approximation can be re-used to define a cheap pruning criterion, which outperforms many existing (more expensive) approaches. We demonstrate the effectiveness of our framework, especially at high sparsity levels, across a range of different neural network architectures and datasets.

In domains with interdependent data, such as graphs, quantifying the epistemic uncertainty of a Graph Neural Network (GNN) is challenging as uncertainty can arise at different structural scales. Existing techniques neglect this issue or only distinguish between structure-aware and structure-agnostic uncertainty without combining them into a single measure. We propose GEBM, an energy-based model (EBM) that provides high-quality uncertainty estimates by aggregating energy at different structural levels that naturally arise from graph diffusion. In contrast to logit-based EBMs, we provably induce an integrable density in the data space by regularizing the energy function. We introduce an evidential interpretation of our EBM that significantly improves the predictive robustness of the GNN. Our framework is a simple and effective post hoc method applicable to any pre-trained GNN that is sensitive to various distribution shifts. It consistently achieves the best separation of in-distribution and out-of-distribution data on 6 out of 7 anomaly types while having the best average rank over shifts on *all* datasets.

Neural wave functions accomplished unprecedented accuracies in approximating the ground state of many-electron systems, though at a high computational cost. Recent works proposed amortizing the cost by learning generalized wave functions across different structures and compounds instead of solving each problem independently. Enforcing the permutation antisymmetry of electrons in such generalized neural wave functions remained challenging as existing methods require discrete orbital selection via non-learnable hand-crafted algorithms. This work tackles the problem by defining overparametrized, fully learnable neural wave functions suitable for generalization across molecules. We achieve this by relying on Pfaffians rather than Slater determinants. The Pfaffian allows us to enforce the antisymmetry on arbitrary electronic systems without any constraint on electronic spin configurations or molecular structure. Our empirical evaluation finds that a single neural Pfaffian calculates the ground state and ionization energies with chemical accuracy across various systems. On the TinyMol dataset, we outperform the `gold-standard' CCSD(T) CBS reference energies by 1.9m$E_h$ and reduce energy errors compared to previous generalized neural wave functions by up to an order of magnitude.

Spatial Message Passing Graph Neural Networks (MPGNNs) are widely used for learning on graph-structured data. However, key limitations of *ℓ*-step MPGNNs are that their "receptive field" is typically limited to the *ℓ*-hop neighborhood of a node and that information exchange between distant nodes is limited by over-squashing. Motivated by these limitations, we propose *Spatio-Spectral Graph Neural Networks (S²GNNs)* – a new modeling paradigm for Graph Neural Networks (GNNs) that synergistically combines spatially and spectrally parametrized graph filters. Parameterizing filters partially in the frequency domain enables global yet efficient information propagation. We show that S²GNNs vanquish over-squashing and yield strictly tighter approximation-theoretic error bounds than MPGNNs. Further, rethinking graph convolutions at a fundamental level unlocks new design spaces. For example, S²GNNs allow for free positional encodings that make them strictly more expressive than the 1-Weisfeiler-Leman (WL) test. Moreover, to obtain general-purpose S²GNNs, we propose spectrally parametrized filters for directed graphs. S²GNNs outperform spatial MPGNNs, graph transformers, and graph rewirings, e.g., on the peptide long-range benchmark tasks, and are competitive with state-of-the-art sequence modeling. On a 40 GB GPU, S²GNNs scale to millions of nodes.

Hierarchical clustering has usually been addressed by discrete optimization using heuristics or continuous optimization of relaxed scores for hierarchies. In this work, we propose to optimize expected scores under a probabilistic model over hierarchies. (1) We show theoretically that the global optimal values of the expected Dasgupta cost and Tree-Sampling divergence (TSD), two unsupervised metrics for hierarchical clustering, are equal to the optimal values of their discrete counterparts contrary to some relaxed scores. (2) We propose Expected Probabilistic Hierarchies (EPH), a probabilistic model to learn hierarchies in data by optimizing expected scores. EPH uses differentiable hierarchy sampling enabling end-to-end gradient descent based optimization, and an unbiased subgraph sampling approach to scale to large datasets. (3) We evaluate EPH on synthetic and real-world datasets including vector and graph datasets. EPH outperforms all other approaches quantitatively and provides meaningful hierarchies in qualitative evaluations.

Amplification by subsampling is one of the main primitives in machine learning with differential privacy (DP): Training a model on random batches instead of complete datasets results in stronger privacy. This is traditionally formalized via mechanism-agnostic subsampling guarantees that express the privacy parameters of a subsampled mechanism as a function of the original mechanism's privacy parameters. We propose the first general framework for deriving mechanism-specific guarantees, which leverage additional information beyond these parameters to more tightly characterize the subsampled mechanism's privacy. Such guarantees are of particular importance for privacy accounting, i.e., tracking privacy over multiple iterations. Overall, our framework based on conditional optimal transport lets us derive existing and novel guarantees for approximate DP, accounting with Renyi DP, and accounting with dominating pairs in a unified, principled manner. As an application, we analyze how subsampling affects the privacy of groups of multiple users. Our tight mechanism-specific bounds outperform tight mechanism-agnostic bounds and classic group privacy results.

Current research in adversarial robustness of LLMs focuses on \textit{discrete} input manipulations in the natural language space, which can be directly transferred to \textit{closed-source} models. However, this approach neglects the steady progression of \textit{open-source} models. As open-source models advance in capability, ensuring their safety becomes increasingly imperative. Yet, attacks tailored to open-source LLMs that exploit full model access remain largely unexplored. We address this research gap and propose the \textit{embedding space attack}, which directly attacks the \textit{continuous} embedding representation of input tokens. We find that embedding space attacks circumvent model alignments and trigger harmful behaviors more efficiently than discrete attacks or model fine-tuning. Additionally, we demonstrate that models compromised by embedding attacks can be used to create discrete jailbreaks in natural language. Lastly, we present a novel threat model in the context of unlearning and show that embedding space attacks can extract supposedly deleted information from unlearned LLMs across multiple datasets and models. Our findings highlight embedding space attacks as an important threat model in open-source LLMs.

Large language models (LLMs) are vulnerable to adversarial attacks that can bypass their safety guardrails. In many domains, adversarial training has proven to be one of the most promising methods to reliably improve robustness against such attacks. Yet, in the context of LLMs, current methods for adversarial training are hindered by the high computational costs required to perform discrete adversarial attacks at each training iteration. We address this problem by instead calculating adversarial attacks in the continuous embedding space of the LLM, which is orders of magnitudes more efficient. We propose a fast adversarial training algorithm (C-AdvUL) composed of two losses: the first makes the model robust on continuous embedding attacks computed on an adversarial behaviour dataset; the second ensures the usefulness of the final model by fine-tuning on utility data. Moreover, we introduce C-AdvIPO, an adversarial variant of IPO that does not require utility data for adversarially robust alignment. Our empirical evaluation on five models from different families (Gemma, Phi3, Mistral, Zephyr, Llama2) and at different scales (2B, 3.8B, 7B) shows that both algorithms substantially enhance LLM robustness against discrete attacks (GCG, AutoDAN, PAIR), while maintaining utility. Our results demonstrate that robustness to continuous perturbations can extrapolate to discrete threat models. Thereby, we present a path toward scalable adversarial training algorithms for robustly aligning LLMs.

Certifying the robustness of machine learning models against domain shifts and input space perturbations is crucial for many applications, where high risk decisions are based on the model’s predictions. Techniques such as randomized smoothing have partially addressed this issues with a focus on adversarial attacks in the past. In this paper, we generalize randomized smoothing to arbitrary transformations and extend it to conformal prediction. The proposed ansatz is demonstrated on a time series classifier connected to an automotive use case. We meticulously assess the robustness of smooth classifiers in environments subjected to various degrees and types of time series native perturbations and compare it against standard conformal predictors. The proposed method consistently offers superior resistance to perturbations, maintaining high classification accuracy and reliability. Additionally, we are able to bound the performance on new domains via calibrating generalization with configuration shifts in the training data. In combination, conformalized randomized smoothing may offer a model agnostic approach to construct robust classifiers tailored to perturbations in their respective applications - a crucial capability for AI assurance argumentation.

Several architecture frameworks for software, systems, and enterprises have been proposed in the literature. They have identified various stakeholders and defined architecture viewpoints and views to frame and address stakeholder concerns. However, the Machine Learning (ML) and data science-related concerns of data scientists and data engineers are yet to be included in existing architecture frameworks. We interviewed 65 experts from around 25 organizations in over ten countries to devise and validate the proposed framework that addresses the mentioned shortcoming.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

Recent neural network-based wave functions have achieved state-of-the-art accuracies in modeling ab-initio ground-state potential energy surface. However, these networks can only solve different spatial arrangements of the same set of atoms. To overcome this limitation, we present Graph-learned orbital embeddings (Globe), a neural network-based reparametrization method that can adapt neural wave functions to different molecules. Globe learns representations of local electronic structures that generalize across molecules via spatial message passing by connecting molecular orbitals to covalent bonds. Further, we propose a size-consistent wave function Ansatz, the Molecular orbital network (Moon), tailored to jointly solve Schrödinger equations of different molecules. In our experiments, we find Moon converging in 4.5 times fewer steps to similar accuracy as previous methods or to lower energies given the same time. Further, our analysis shows that Moon's energy estimate scales additively with increased system sizes, unlike previous work where we observe divergence. In both computational chemistry and machine learning, we are the first to demonstrate that a single wave function can solve the Schrödinger equation of molecules with different atoms jointly.

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains, including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian — a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). Across all models and datasets, we observe robust improvements in energy mean absolute errors, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground-truth energy.

Graph Neural Networks (GNNs) are promising surrogates for quantum mechanical calculations as they establish unprecedented low errors on collections of molecular dynamics (MD) trajectories. Thanks to their fast inference times they promise to accelerate computational chemistry applications. Unfortunately, despite low in-distribution (ID) errors, such GNNs might be horribly wrong for out-of-distribution (OOD) samples. Uncertainty estimation (UE) may aid in such situations by communicating the model’s certainty about its prediction. Here, we take a closer look at the problem and identify six key desiderata for UE in molecular force fields, three ’physics-informed’ and three ’application-focused’ ones. To overview the field, we survey existing methods from the field of UE and analyze how they fit to the set desiderata. By our analysis, we conclude that none of the previous works satisfies all criteria. To fill this gap, we propose Localized Neural Kernel (LNK) a Gaussian Process (GP)-based extension to existing GNNs satisfying the desiderata. In our extensive experimental evaluation, we test four different UE with three different backbones across two datasets. In out-of-equilibrium detection, we find LNK yielding up to 2.5 and 2.1 times lower errors in terms of AUC-ROC score than dropout or evidential regression-based methods while maintaining high predictive performance.

The ability to detect learned objects regardless of their appearance is crucial for autonomous systems in real-world applications. Especially for detecting humans, which is often a fundamental task in safety-critical applications, it is vital to prevent errors. To address this challenge, we propose a self-monitoring framework that allows for the perception system to perform plausibility checks at runtime. We show that by incorporating an additional component for detecting human body parts, we are able to significantly reduce the number of missed human detections by factors of up to 9 when compared to a baseline setup, which was trained only on holistic person objects. Additionally, we found that training a model jointly on humans and their body parts leads to a substantial reduction in false positive detections by up to 50% compared to training on humans alone. We performed comprehensive experiments on the publicly available datasets DensePose and Pascal VOC in order to demonstrate the effectiveness of our framework. Code is available at https://github.com/FraunhoferIKS/smf-object-detection.

Despite its success in the image domain, adversarial training did not (yet) stand out as an effective defense for Graph Neural Networks (GNNs) against graph structure perturbations. In the pursuit of fixing adversarial training (1) we show and overcome fundamental theoretical as well as practical limitations of the adopted graph learning setting in prior work; (2) we reveal that flexible GNNs based on learnable graph diffusion are able to adjust to adversarial perturbations, while the learned message passing scheme is naturally interpretable; (3) we introduce the first attack for structure perturbations that, while targeting multiple nodes at once, is capable of handling global (graph-level) as well as local (node-level) constraints. Including these contributions, we demonstrate that adversarial training is a state-of-the-art defense against adversarial structure perturbations.

Autoregressive neural networks within the temporal point process (TPP) framework have become the standard for modeling continuous-time event data. Even though these models can expressively capture event sequences in a one-step-ahead fashion, they are inherently limited for long-term forecasting applications due to the accumulation of errors caused by their sequential nature. To overcome these limitations, we derive ADD-THIN, a principled probabilistic denoising diffusion model for TPPs that operates on entire event sequences. Unlike existing diffusion approaches, ADD-THIN naturally handles data with discrete and continuous components. In experiments on synthetic and real-world datasets, our model matches the state-of-the-art TPP models in density estimation and strongly outperforms them in forecasting.

Real-world data is complex and often consists of objects that can be decomposed into multiple entities (e.g. images into pixels, graphs into interconnected nodes). Randomized smoothing is a powerful framework for making models provably robust against small changes to their inputs - by guaranteeing robustness of the majority vote when randomly adding noise before classification. Yet, certifying robustness on such complex data via randomized smoothing is challenging when adversaries do not arbitrarily perturb entire objects (e.g. images) but only a subset of their entities (e.g. pixels). As a solution, we introduce hierarchical randomized smoothing: We partially smooth objects by adding random noise only on a randomly selected subset of their entities. By adding noise in a more targeted manner than existing methods we obtain stronger robustness guarantees while maintaining high accuracy. We initialize hierarchical smoothing using different noising distributions, yielding novel robustness certificates for discrete and continuous domains. We experimentally demonstrate the importance of hierarchical smoothing in image and node classification, where it yields superior robustness-accuracy trade-offs. Overall, hierarchical smoothing is an important contribution towards models that are both - certifiably robust to perturbations and accurate.

A machine learning model is traditionally considered robust if its prediction remains (almost) constant under input perturbations with small norm. However, real-world tasks like molecular property prediction or point cloud segmentation have inherent equivariances, such as rotation or permutation equivariance. In such tasks, even perturbations with large norm do not necessarily change an input's semantic content. Furthermore, there are perturbations for which a model's prediction explicitly needs to change. For the first time, we propose a sound notion of adversarial robustness that accounts for task equivariance. We then demonstrate that provable robustness can be achieved by (1) choosing a model that matches the task's equivariances (2) certifying traditional adversarial robustness. Certification methods are, however, unavailable for many models, such as those with continuous equivariances. We close this gap by developing the framework of equivariance-preserving randomized smoothing, which enables architecture-agnostic certification. We additionally derive the first architecture-specific graph edit distance certificates, i.e. sound robustness guarantees for isomorphism equivariant tasks like node classification. Overall, a sound notion of robustness is an important prerequisite for future work at the intersection of robust and geometric machine learning.

Consensus clustering is gaining increasing attention for its high quality and robustness. In particular, k -means-based Consensus Clustering (KCC) converts the usual computationally expensive problem to a classic k -means clustering with generalized utility functions, bringing potentials for large-scale data clustering on different types of data. Despite KCC’s applicability and generalizability, implementing this method such as representing the binary dataset in the k -means heuristic is challenging and has seldom been discussed in prior work. To fill this gap, we present a MATLAB package, KCC, that completely implements the KCC framework and utilizes a sparse representation technique to achieve a low space complexity. Compared to alternative consensus clustering packages, the KCC package is of high flexibility, efficiency, and effectiveness. Extensive numerical experiments are also included to show its usability on real-world datasets.

Software engineering of network-centric Artificial Intelligence (AI) and Internet of Things (IoT) enabled Cyber-Physical Systems (CPS) and services, involves complex design and validation challenges. In this paper, we propose a novel approach, based on the model-driven software engineering paradigm, in particular the domain-specific modeling methodology. We focus on a sub-discipline of AI, namely Machine Learning (ML) and propose the delegation of data analytics and ML to the IoT edge. This way, we may increase the service quality of ML, for example, its availability and performance, regardless of the network conditions, as well as maintaining the privacy, security and sustainability. We let practitioners assign ML tasks to heterogeneous edge devices, including highly resource-constrained embedded microcontrollers with main memories in the order of Kilobytes, and energy consumption in the order of milliwatts. This is known as Tiny ML. Furthermore, we show how software models with different levels of abstraction, namely platform-independent and platform-specific models can be used in the software development process. Finally, we validate the proposed approach using a case study addressing the predictive maintenance of a hydraulics system with various networked sensors and actuators.

Pruning, the task of sparsifying deep neural networks, received increasing attention recently. Although state-of-the-art pruning methods extract highly sparse models, they neglect two main challenges: (1) the process of finding these sparse models is often very expensive; (2) unstructured pruning does not provide benefits in terms of GPU memory, training time, or carbon emissions. We propose Early Compression via Gradient Flow Preservation (EarlyCroP), which efficiently extracts state-of-the-art sparse models before or early in training addressing challenge (1), and can be applied in a structured manner addressing challenge (2). This enables us to train sparse networks on commodity GPUs whose dense versions would be too large, thereby saving costs and reducing hardware requirements. We empirically show that EarlyCroP outperforms a rich set of baselines for many tasks (incl. classification, regression) and domains (incl. computer vision, natural language processing, and reinforcment learning). EarlyCroP leads to accuracy comparable to dense training while outperforming pruning baselines.

Molecular property prediction is one of the fastest-growing applications of deep learning with critical real-world impacts. Although the 3D molecular graph structure is necessary for models to achieve strong performance on many tasks, it is infeasible to obtain 3D structures at the scale required by many real-world applications. To tackle this issue, we propose to use existing 3D molecular datasets to pre-train a model to reason about the geometry of molecules given only their 2D molecular graphs. Our method, called 3D Infomax, maximizes the mutual information between learned 3D summary vectors and the representations of a graph neural network (GNN). During fine-tuning on molecules with unknown geometry, the GNN is still able to produce implicit 3D information and uses it for downstream tasks. We show that 3D Infomax provides significant improvements for a wide range of properties, including a 22% average MAE reduction on QM9 quantum mechanical properties. Moreover, the learned representations can be effectively transferred between datasets in different molecular spaces.

Randomized smoothing is currently considered the state-of-the-art method to obtain certifiably robust classifiers. Despite its remarkable performance, the method is associated with various serious problems such as “certified accuracy waterfalls”, certification vs. accuracy trade-off, or even fairness issues. Input-dependent smoothing approaches have been proposed with intention of overcoming these flaws. However, we demonstrate that these methods lack formal guarantees and so the resulting certificates are not justified. We show that in general, the input-dependent smoothing suffers from the curse of dimensionality, forcing the variance function to have low semi-elasticity. On the other hand, we provide a theoretical and practical framework that enables the usage of input-dependent smoothing even in the presence of the curse of dimensionality, under strict restrictions. We present one concrete design of the smoothing variance function and test it on CIFAR10 and MNIST. Our design mitigates some of the problems of classical smoothing and is formally underlined, yet further improvement of the design is still necessary.

Safe navigation is one of the steps necessary for achieving autonomous control of robots. Among different algorithms that focus on robot navigation, Reinforcement Learning (and more specifically Deep Reinforcement Learning) has shown impressive results for controlling robots with complex and high-dimensional state representations. However, when integrating methods to comply with safety requirements by means of constraint satisfaction in flat Reinforcement Learning policies, the system performance can be affected. In this paper, we propose a constrained Hierarchical Reinforcement Learning framework with a safety layer used to modify the low-level policy to achieve a safer operation of the robot. Results obtained in simulation show that the proposed method is better at retaining performance while keeping the system in a safe region when compared to a constrained flat model.

Single-cell transcriptomics enabled the study of cellular heterogeneity in response to perturbations at the resolution of individual cells. However, scaling high-throughput screens (HTSs) to measure cellular responses for many drugs remains a challenge due to technical limitations and, more importantly, the cost of such multiplexed experiments. Thus, transferring information from routinely performed bulk RNA HTS is required to enrich single-cell data meaningfully.We introduce chemCPA, a new encoder-decoder architecture to study the perturbational effects of unseen drugs. We combine the model with an architecture surgery for transfer learning and demonstrate how training on existing bulk RNA HTS datasets can improve generalisation performance. Better generalisation reduces the need for extensive and costly screens at single-cell resolution. We envision that our proposed method will facilitate more efficient experiment designs through its ability to generate in-silico hypotheses, ultimately accelerating drug discovery.

A cursory reading of the literature suggests that we have made a lot of progress in designing effective adversarial defenses for Graph Neural Networks (GNNs). Yet, the standard methodology has a serious flaw – virtually all of the defenses are evaluated against non-adaptive attacks leading to overly optimistic robustness estimates. We perform a thorough robustness analysis of 7 of the most popular defenses spanning the entire spectrum of strategies, i.e., aimed at improving the graph, the architecture, or the training. The results are sobering – most defenses show no or only marginal improvement compared to an undefended baseline. We advocate using custom adaptive attacks as a gold standard and we outline the lessons we learned from successfully designing such attacks. Moreover, our diverse collection of perturbed graphs forms a (black-box) unit test offering a first glance at a model's robustness.

Randomized smoothing is one of the most promising frameworks for certifying the adversarial robustness of machine learning models, including Graph Neural Networks (GNNs). Yet, existing randomized smoothing certificates for GNNs are overly pessimistic since they treat the model as a black box, ignoring the underlying architecture. To remedy this, we propose novel gray-box certificates that exploit the message-passing principle of GNNs: We randomly intercept messages and carefully analyze the probability that messages from adversarially controlled nodes reach their target nodes. Compared to existing certificates, we certify robustness to much stronger adversaries that control entire nodes in the graph and can arbitrarily manipulate node features. Our certificates provide stronger guarantees for attacks at larger distances, as messages from farther-away nodes are more likely to get intercepted. We demonstrate the effectiveness of our method on various models and datasets. Since our gray-box certificates consider the underlying graph structure, we can significantly improve certifiable robustness by applying graph sparsification.

Building models that comply with the invariances inherent to different domains, such as invariance under translation or rotation, is a key aspect of applying machine learning to real world problems like molecular property prediction, medical imaging, protein folding or LiDAR classification. For the first time, we study how the invariances of a model can be leveraged to provably guarantee the robustness of its predictions. We propose a gray-box approach, enhancing the powerful black-box randomized smoothing technique with white-box knowledge about invariances. First, we develop gray-box certificates based on group orbits, which can be applied to arbitrary models with invariance under permutation and Euclidean isometries. Then, we derive provably tight gray-box certificates. We experimentally demonstrate that the provably tight certificates can offer much stronger guarantees, but that in practical scenarios the orbit-based method is a good approximation.

Abstract Many systems can be expressed as multivariate state sequences (MSS) in terms of entities and their states with evolving dependencies over time. In order to interpret the temporal dynamics in such data, it is essential to capture relationships between entities and their changes in state and dependence over time under uncertainty. Existing probabilistic models do not explicitly model the evolution of causality between dependent state sequences and mostly result in complex structures when representing complete causal dependencies between random variables. To solve this, Temporal State Change Bayesian Networks (TSCBN) are introduced to effectively model interval relations of MSSs under evolving uncertainty. Our model outperforms competing approaches in terms of parameter complexity and expressiveness. Further, an efficient structure discovery method for TSCBNs is presented, that improves classical approaches by exploiting temporal knowledge and multiple parameter estimation approaches for TSCBNs are introduced. Those are expectation maximization, variational inference and a sampling based maximum likelihood estimation that allow to learn parameters from partially observed MSSs. Lastly, we demonstrate how TSCBNs allow to interpret and infer patterns of captured sequences for specification mining in automotive.

Abstract In machine learning, continuously retraining a model guarantees accurate predictions based on the latest data as training input. But to retrieve the latest data from a database, time-consuming extraction is necessary as database systems have rarely been used for operations such as matrix algebra and gradient descent. In this work, we demonstrate that SQL with recursive tables makes it possible to express a complete machine learning pipeline out of data preprocessing, model training and its validation. To facilitate the specification of loss functions, we extend the code-generating database system Umbra by an operator for automatic differentiation for use within recursive tables: With the loss function expressed in SQL as a lambda function, Umbra generates machine code for each partial derivative. We further use automatic differentiation for a dedicated gradient descent operator, which generates LLVM code to train a user-specified model on GPUs. We fine-tune GPU kernels at hardware level to allow a higher throughput and propose non-blocking synchronisation of multiple units. In our evaluation, automatic differentiation accelerated the runtime by the number of cached subexpressions compared to compiling each derivative separately. Our GPU kernels with independent models allowed maximal throughput even for small batch sizes, making machine learning pipelines within SQL more competitive.

Abstract Neural networks are known to be sensitive to adversarial perturbations. To investigate this undesired behavior we consider the problem of computing the distance to the decision boundary (DtDB) from a given sample for a deep neural net classifier. In this work we present a procedure where we solve a convex quadratic programming (QP) task to obtain a lower bound on the DtDB. This bound is used as a robustness certificate of the classifier around a given sample. We show that our approach provides better or competitive results in comparison with a wide range of existing techniques.

Abstract Models are used in both Software Engineering (SE) and Artificial Intelligence (AI). SE models may specify the architecture at different levels of abstraction and for addressing different concerns at various stages of the software development life-cycle, from early conceptualization and design, to verification, implementation, testing and evolution. However, AI models may provide smart capabilities, such as prediction and decision-making support. For instance, in Machine Learning (ML), which is currently the most popular sub-discipline of AI, mathematical models may learn useful patterns in the observed data and can become capable of making predictions. The goal of this work is to create synergy by bringing models in the said communities together and proposing a holistic approach to model-driven software development for intelligent systems that require ML. We illustrate how software models can become capable of creating and dealing with ML models in a seamless manner. The main focus is on the domain of the Internet of Things (IoT), where both ML and model-driven SE play a key role. In the context of the need to take a Cyber-Physical System-of-Systems perspective of the targeted architecture, an integrated design environment for both SE and ML sub-systems would best support the optimization and overall efficiency of the implementation of the resulting system. In particular, we implement the proposed approach, called ML-Quadrat, based on ThingML, and validate it using a case study from the IoT domain, as well as through an empirical user evaluation. It transpires that the proposed approach is not only feasible, but may also contribute to the performance leap of software development for smart Cyber-Physical Systems (CPS) which are connected to the IoT, as well as an enhanced user experience of the practitioners who use the proposed modeling solution.

Augmented reality applications use object tracking to estimate the pose of a camera and to superimpose virtual content onto the observed object. Today, a number of tracking systems are available, ready to be used in industrial applications. However, such systems are hard to handle for a service maintenance engineer, due to obscure configuration procedures. In this article, we investigate options towards replacing the manual configuration process with a machine learning approach based on automatically synthesized data. We present an automated process of creating object tracker facilities exclusively from synthetic data. The data is highly enhanced to train a convolutional neural network, while still being able to receive reliable and robust results during real world applications only from simple RGB cameras. Comparison against related work using the LINEMOD dataset showed that we are able to outperform similar approaches. For our intended industrial applications with high accuracy demands, its performance is still lower than common object tracking methods with manual configuration. Yet, it can greatly support those as an add-on during initialization, due to its higher reliability.

Randomized smoothing is currently the most competitive technique for providing provable robustness guarantees. Since this approach is model-agnostic and inherently scalable we can certify arbitrary classifiers. Despite its success, recent works show that for a small class of i.i.d. distributions, the largest $l_p$ radius that can be certified using randomized smoothing decreases as $O(1/d^{1/2-1/p})$ with dimension $d$ for $p > 2$. We complete the picture and show that similar no-go results hold for the $l_2$ norm for a much more general family of distributions which are continuous and symmetric about the origin. Specifically, we calculate two different upper bounds of the $l_2$ certified radius which have a constant multiplier of order $\Theta(1/d^{1/2})$. Moreover, we extend our results to $l_p (p>2)$ certification with spherical symmetric distributions solidifying the limitations of randomized smoothing. We discuss the implications of our results for how accuracy and robustness are related, and why robust training with noise augmentation can alleviate some of the limitations in practice. We also show that on real-world data the gap between the certified radius and our upper bounds is small.

Modeling sets is an important problem in machine learning since this type of data can be found in many domains. A promising approach defines a family of permutation invariant densities with continuous normalizing flows. This allows us to maximize the likelihood directly and sample new realizations with ease. In this work, we demonstrate how calculating the trace, a crucial step in this method, raises issues that occur both during training and inference, limiting its practicality. We propose an alternative way of defining permutation equivariant transformations that give closed form trace. This leads not only to improvements while training, but also to better final performance. We demonstrate the benefits of our approach on point processes and general set modeling.

Dirichlet-based uncertainty (DBU) models are a recent and promising class of uncertainty-aware models. DBU models predict the parameters of a Dirichlet distribution to provide fast, high-quality uncertainty estimates alongside with class predictions. In this work, we present the first large-scale, in-depth study of the robustness of DBU models under adversarial attacks. Our results suggest that uncertainty estimates of DBU models are not robust w.r.t. three important tasks: (1) indicating correctly and wrongly classified samples; (2) detecting adversarial examples; and (3) distinguishing between in-distribution (ID) and out-of-distribution (OOD) data. Additionally, we explore the first approaches to make DBU mod- els more robust. While adversarial training has a minor effect, our median smoothing based ap- proach significantly increases robustness of DBU models.

Temporal point processes (TPP) are probabilistic generative models for continuous-time event sequences. Neural TPPs combine the fundamental ideas from point process literature with deep learning approaches, thus enabling construction of flexible and efficient models. The topic of neural TPPs has attracted significant attention in the recent years, leading to the development of numerous new architectures and applications for this class of models. In this review paper we aim to consolidate the existing body of knowledge on neural TPPs. Specifically, we focus on important design choices and general principles for defining neural TPP models. Next, we provide an overview of application areas commonly considered in the literature. We conclude this survey with the list of open challenges and important directions for future work in the field of neural TPPs.

Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose an alternative by directly modeling the solution curves - the flow of an ODE - with a neural network. This immediately eliminates the need for expensive numerical solvers while still maintaining the modeling capability of neural ODEs. We propose several flow architectures suitable for different applications by establishing precise conditions on when a function defines a valid flow. Apart from computational efficiency, we also provide empirical evidence of favorable generalization performance via applications in time series modeling, forecasting, and density estimation.

Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes for this task, overtaking classical methods based on fixed molecular kernels. However, they still appear very limited from a theoretical perspective, since regular GNNs cannot distinguish certain types of graphs. In this work we close this gap between theory and practice. We show that GNNs with directed edge embeddings and two-hop message passing are indeed universal approximators for predictions that are invariant to translation, and equivariant to permutation and rotation. We then leverage these insights and multiple structural improvements to propose the geometric message passing neural network (GemNet). We demonstrate the benefits of the proposed changes in multiple ablation studies. GemNet outperforms previous models on the COLL, MD17, and OC20 datasets by 34%, 41%, and 20%, respectively, and performs especially well on the most challenging molecules. Our implementation is available online.

Graph neural networks that leverage coordinates via directional message passing have recently set the state of the art on multiple molecular property prediction tasks. However, they rely on atom position information that is often unavailable, and obtaining it is usually prohibitively expensive or even impossible. In this paper we propose synthetic coordinates that enable the use of advanced GNNs without requiring the true molecular configuration. We propose two distances as synthetic coordinates: Distance bounds that specify the rough range of molecular configurations, and graph-based distances using a symmetric variant of personalized PageRank. To leverage both distance and angular information we propose a method of transforming normal graph neural networks into directional MPNNs. We show that with this transformation we can reduce the error of a normal graph neural network by 55% on the ZINC benchmark. We furthermore set the state of the art on ZINC and coordinate-free QM9 by incorporating synthetic coordinates in the SMP and DimeNet++ models. Our implementation is available online.

Graph Neural Networks (GNNs) are increasingly important given their popularity and the diversity of applications. Yet, existing studies of their vulnerability to adversarial attacks rely on relatively small graphs. We address this gap and study how to attack and defend GNNs at scale. We propose two sparsity-aware first-order optimization attacks that maintain an efficient representation despite optimizing over a number of parameters which is quadratic in the number of nodes. We show that common surrogate losses are not well-suited for global attacks on GNNs. Our alternatives can double the attack strength. Moreover, to improve GNNs' reliability we design a robust aggregation function, Soft Median, resulting in an effective defense at all scales. We evaluate our attacks and defense with standard GNNs on graphs more than 100 times larger compared to previous work. We even scale one order of magnitude further by extending our techniques to a scalable GNN.

Automatically detecting anomalies in event data can provide substantial value in domains such as healthcare, DevOps, and information security. In this paper, we frame the problem of detecting anomalous continuous-time event sequences as out-of-distribution (OOD) detection for temporal point processes (TPPs). First, we show how this problem can be approached using goodness-of-fit (GoF) tests. We then demonstrate the limitations of popular GoF statistics for TPPs and propose a new test that addresses these shortcomings. The proposed method can be combined with various TPP models, such as neural TPPs, and is easy to implement. In our experiments, we show that the proposed statistic excels at both traditional GoF testing, as well as at detecting anomalies in simulated and real-world data.

The interdependence between nodes in graphs is key to improve class prediction on nodes, utilized in approaches like Label Probagation (LP) or in Graph Neural Networks (GNNs). Nonetheless, uncertainty estimation for non-independent node-level predictions is under-explored. In this work, we explore uncertainty quantification for node classification in three ways: (1) We derive three axioms explicitly characterizing the expected predictive uncertainty behavior in homophilic attributed graphs.(2) We propose a new model Graph Posterior Network (GPN) which explicitly performs Bayesian posterior updates for predictions on interdependent nodes. GPN provably obeys the proposed axioms. (3) We extensively evaluate GPN and a strong set of baselines on semi-supervised node classification including detection of anomalous features, and detection of left-out classes. GPN outperforms existing approaches for uncertainty estimation in the experiments.

Abstract Visual Question Answering (VQA) is concerned with answering free-form questions about an image. Since it requires a deep semantic and linguistic understanding of the question and the ability to associate it with various objects that are present in the image, it is an ambitious task and requires multi-modal reasoning from both computer vision and natural language processing. We propose Graphhopper, a novel method that approaches the task by integrating knowledge graph reasoning, computer vision, and natural language processing techniques. Concretely, our method is based on performing context-driven, sequential reasoning based on the scene entities and their semantic and spatial relationships. As a first step, we derive a scene graph that describes the objects in the image, as well as their attributes and their mutual relationships. Subsequently, a reinforcement learning agent is trained to autonomously navigate in a multi-hop manner over the extracted scene graph to generate reasoning paths, which are the basis for deriving answers. We conduct an experimental study on the challenging dataset GQA, based on both manually curated and automatically generated scene graphs. Our results show that we keep up with human performance on manually curated scene graphs. Moreover, we find that Graphhopper outperforms another state-of-the-art scene graph reasoning model on both manually curated and automatically generated scene graphs by a significant margin.

In machine learning, continuously retraining a model guarantees accurate predictions based on the latest data as training input. But to retrieve the latest data from a database, time-consuming extraction is necessary as database systems have rarely been used for operations such as matrix algebra and gradient descent.

Abstract Finding communities that are not only relatively densely connected in a graph but that also show similar characteristics based on attribute information has drawn strong attention in the last years. There exists already a remarkable body of work that attempts to find communities in vertex-attributed graphs that are relatively homogeneous with respect to attribute values. Yet, it is scattered through different research fields and most of those publications fail to make the connection. In this paper, we identify important characteristics of the different approaches and place them into three broad categories: those that selectdescriptive attributes, related to clustering approaches, those that enumerateattribute-value combinations, related to pattern mining techniques, and those that identify conditional attribute weights, allowing for post-processing. We point out that the large majority of these techniques treat the same problem in terms of attribute representation, and are therefore interchangeable to a certain degree. In addition, different authors have found very similar algorithmic solutions to their respective problem.

Abstract Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and reliability of predictions. We answer these questions by computing reachable sets of neural networks, i.e. sets of outputs resulting from continuous sets of inputs. We provide two efficient approaches that lead to over- and under-approximations of the reachable set. This principle is highly versatile, as we show. First, we use it to analyze and enhance the robustness properties of both classifiers and regression models. This is in contrast to existing works, which are mainly focused on classification. Specifically, we verify (non-)robustness, propose a robust training procedure, and show that our approach outperforms adversarial attacks as well as state-of-the-art methods of verifying classifiers for non-norm bound perturbations. Second, we provide techniques to distinguish between reliable and non-reliable predictions for unlabeled inputs, to quantify the influence of each feature on a prediction, and compute a feature ranking.

The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central group is -hard. As a result, approximation algorithms to maximize group centralities were introduced recently. Despite a nearly-linear running time, approximation algorithms for group betweenness and (to a lesser extent) group closeness are rather slow on large networks due to high constant overheads. That is why we introduce GED-Walk centrality, a new submodular group centrality measure inspired by Katz centrality. In contrast to closeness and betweenness, it considers walks of any length rather than shortest paths, with shorter walks having a higher contribution. We define algorithms that (i) efficiently approximate the GED-Walk score of a given group and (ii) efficiently approximate the (proved to be -hard) problem of finding a group with highest GED-Walk score. Experiments on several real-world datasets show that scores obtained by GED-Walk improve performance on common graph mining tasks such as collective classification and graph-level classification. An evaluation of empirical running times demonstrates that maximizing GED-Walk (in approximation) is two orders of magnitude faster compared to group betweenness approximation and for group sizes ≤ 100 one to two orders faster than group closeness approximation. For graphs with tens of millions of edges, approximate GED-Walk maximization typically needs less than one minute. Furthermore, our experiments suggest that the maximization algorithms scale linearly with the size of the input graph and the size of the group.

Existing techniques for certifying the robustness of models for discrete data either work only for a small class of models or are general at the expense of efficiency or tightness. Moreover, they do not account for sparsity in the input which, as our findings show, is often essential for obtaining non-trivial guarantees. We propose a model-agnostic certificate based on the randomized smoothing framework which subsumes earlier work and is tight, efficient, and sparsity-aware. Its computational complexity does not depend on the number of discrete categories or the dimension of the input (e.g. the graph size), making it highly scalable. We show the effectiveness of our approach on a wide variety of models, datasets, and tasks – specifically highlighting its use for Graph Neural Networks. So far, obtaining provable guarantees for GNNs has been difficult due to the discrete and non-i.i.d. nature of graph data. Our method can certify any GNN and handles perturbations to both the graph structure and the node attributes.

Graph neural networks (GNNs) have emerged as a powerful approach for solving many network mining tasks. However, learning on large graphs remains a challenge -- many recently proposed scalable GNN approaches rely on an expensive message-passing procedure to propagate information through the graph. We present the PPRGo model which utilizes an efficient approximation of information diffusion in GNNs resulting in significant speed gains while maintaining state-of-the-art prediction performance. In addition to being faster, PPRGo is inherently scalable, and can be trivially parallelized for large datasets like those found in industry settings.

Recent works show that message-passing neural networks (MPNNs) can be fooled by adversarial attacks on both the node attributes and the graph structure. Since MPNNs are currently being rapidly adopted in real-world applications, it is thus crucial to improve their reliablility and robustness. While there has been progress on robustness certification of MPNNs under perturbation of the node attributes, no existing method can handle structural perturbations. These perturbations are especially challenging because they alter the message passing scheme itself. In this work we close this gap and propose the first method to certify robustness of Graph Convolutional Networks (GCNs) under perturbations of the graph structure. We show how this problem can be expressed as a jointly constrained bilinear program - a challenging, yet well-studied class of problems - and propose a novel branch-and-bound algorithm to obtain lower bounds on the global optimum. These lower bounds are significantly tighter and can certify up to twice as many nodes compared to a standard linear relaxation.

Accurate estimation of aleatoric and epistemic uncertainty is crucial to build safe and reliable systems. Traditional approaches, such as dropout and ensemble methods, estimate uncertainty by sampling probability predictions from different submodels, which leads to slow uncertainty estimation at inference time. Recent works address this drawback by directly predicting parameters of prior distributions over the probability predictions with a neural network. While this approach has demonstrated accurate uncertainty estimation, it requires defining arbitrary target parameters for in-distribution data and makes the unrealistic assumption that out-of-distribution (OOD) data is known at training time. In this work we propose the Posterior Network (PostNet), which uses Normalizing Flows to predict an individual closed-form posterior distribution over predicted probabilites for any input sample. The posterior distributions learned by PostNet accurately reflect uncertainty for in- and out-of-distribution data -- without requiring access to OOD data at training time. PostNet achieves state-of-the art results in OOD detection and in uncertainty calibration under dataset shifts.

Perturbations targeting the graph structure have proven to be extremely effective in reducing the performance of Graph Neural Networks (GNNs), and traditional defenses such as adversarial training do not seem to be able to improve robustness. This work is motivated by the observation that adversarially injected edges effectively can be viewed as additional samples to a node's neighborhood aggregation function, which results in distorted aggregations accumulating over the layers. Conventional GNN aggregation functions, such as a sum or mean, can be distorted arbitrarily by a single outlier. We propose a robust aggregation function motivated by the field of robust statistics. Our approach exhibits the largest possible breakdown point of 0.5, which means that the bias of the aggregation is bounded as long as the fraction of adversarial edges of a node is less than 50%. Our novel aggregation function, Soft Medoid, is a fully differentiable generalization of the Medoid and therefore lends itself well for end-to-end deep learning. Equipping a GNN with our aggregation improves the robustness with respect to structure perturbations on Cora ML by a factor of 3 (and 5.5 on Citeseer) and by a factor of 8 for low-degree nodes.

This work addresses efficient inference and learning in switching Gaussian linear dynamical systems using a Rao-Blackwellised particle filter and a corresponding Monte Carlo objective. To improve the forecasting capabilities, we extend this classical model by conditionally linear state-to-switch dynamics, while leaving the partial tractability of the conditional Gaussian linear part intact. Furthermore, we use an auxiliary variable approach with a decoder-type neural network that allows for more complex non-linear emission models and multivariate observations. We propose a Monte Carlo objective that leverages the conditional linearity by computing the corresponding conditional expectations in closed-form and a suitable proposal distribution that is factorised similarly to the optimal proposal distribution. We evaluate our approach on several popular time series forecasting datasets as well as image streams of simulated physical systems. Our results show improved forecasting performance compared to other deep state-space model approaches.

Temporal point process (TPP) models combined with recurrent neural networks provide a powerful framework for modeling continuous-time event data. While such models are flexible, they are inherently sequential and therefore cannot benefit from the parallelism of modern hardware. By exploiting the recent developments in the field of normalizing flows, we design TriTPP - a new class of non-recurrent TPP models, where both sampling and likelihood computation can be done in parallel. TriTPP matches the flexibility of RNN-based methods but permits several orders of magnitude faster sampling. This enables us to use the new model for variational inference in continuous-time discrete-state systems. We demonstrate the advantages of the proposed framework on synthetic and real-world datasets.

Deep learning models for graphs have achieved strong performance for the task of node classification. Despite their proliferation, little is known about their robustness to adversarial attacks. Yet, in domains where they are likely to be used, e.g., the web, adversaries are common. Can deep learning models for graphs be easily fooled? In this work, we present a study of adversarial attacks on attributed graphs, specifically focusing on models exploiting ideas of graph convolutions. In addition to attacks at test time, we tackle the more challenging class of poisoning/causative attacks, which focus on the training phase of a machine learning model. We generate adversarial perturbations targeting the node’s features and the graph structure , thus, taking the dependencies between instances in account. Moreover, we ensure that the perturbations remain unnoticeable by preserving important data characteristics. To cope with the underlying discrete domain, we propose an efficient algorithm N ettack exploiting incremental computations. Our experimental study shows that accuracy of node classification significantly drops even when performing only few perturbations. Even more, our attacks are transferable: the learned attacks generalize to other state-of-the-art node classification models and unsupervised approaches, and likewise are successful even when only limited knowledge about the graph is given. For the first time, we successfully identify important patterns of adversarial attacks on graph neural networks (GNNs) — a first step towards being able to detect adversarial attacks on GNNs.

Learning from multiple sources of information is an important problem in machine-learning research. The key challenges are learning representations and formulating inference methods that take into account the complementarity and redundancy of various information sources. In this paper we formulate a variational autoencoder based multi-source learning framework in which each encoder is conditioned on a different information source. This allows us to relate the sources via the shared latent variables by computing divergence measures between individual source’s posterior approximations. We explore a variety of options to learn these encoders and to integrate the beliefs they compute into a consistent posterior approximation. We visualise learned beliefs on a toy dataset and evaluate our methods for learning shared representations and structured output prediction, showing trade-offs of learning separate encoders for each information source. Furthermore, we demonstrate how conflict detection and redundancy can increase robustness of inference in a multi-source setting.

Verification is essential to prevent malfunctioning of software systems. Model checking allows to verify conformity with nominal behavior. As manual definition of specifications from such systems gets infeasible, automated techniques to mine specifications from data become increasingly important. Existing approaches produce specifications of limited lengths, do not segregate functions and do not easily allow to include expert input. We present BaySpec, a dynamic mining approach to extract temporal specifications from Bayesian models, which represent behavioral patterns. This allows to learn specifications of arbitrary length from imperfect traces. Within this framework we introduce a novel extraction algorithm that for the first time mines LTL specifications from such models.

This work demonstrates a wide range of applications that use lambda expressions in SQL. Such injected code snippets form a useful technique required by data mining algorithms to overcome the inflexibility of the SQL language, as the language is limited to predefined aggregations only. Following the ’move computation to the data’ paradigm, we extend SQL lambda functions - also known from common programming languages - for machine- learning tasks.\n\nAs machine-learning relies mostly on gradient descent and tensor data types, we use lambda expressions for clustering and graph-mining algorithms as well as to formulate loss functions and label data. To underline the flexibility gained in SQL, this work demonstrates a main memory database system with integrated lambda expressions accessible through table functions in SQL. By reusing SQL and performing data mining and machine- learning tasks faster than can dedicated tools, this demonstration aims at convincing data scientists of the capabilities of database systems for computational tasks.

The goal of network representation learning is to learn low-dimensional node embeddings that capture the graph structure and are useful for solving downstream tasks. However, despite the proliferation of such methods, there is currently no study of their robustness to adversarial attacks. We provide the first adversarial vulnerability analysis on the widely used family of methods based on random walks. We derive efficient adversarial perturbations that poison the network structure and have a negative effect on both the quality of the embeddings and the downstream tasks. We further show that our attacks are transferable since they generalize to many models and are successful even when the attacker is restricted.

Deep learning models for graphs have achieved strong performance for the task of node classification. Despite their proliferation, currently there is no study of their robustness to adversarial attacks. Yet, in domains where they are likely to be used, e.g. the web, adversaries are common. Can deep learning models for graphs be easily fooled? In this extended abstract we summarize the key findings and contributions of our work, in which we introduce the first study of adversarial attacks on attributed graphs, specifically focusing on models exploiting ideas of graph convolutions. In addition to attacks at test time, we tackle the more challenging class of poisoning/causative attacks, which focus on the training phase of a machine learning model. We generate adversarial perturbations targeting the node's features and the graph structure, thus, taking the dependencies between instances in account. Moreover, we ensure that the perturbations remain unnoticeable by preserving important data characteristics. To cope with the underlying discrete domain we propose an efficient algorithm Nettack exploiting incremental computations. Our experimental study shows that accuracy of node classification significantly drops even when performing only few perturbations. Even more, our attacks are transferable: the learned attacks generalize to other state-of-the-art node classification models and unsupervised approaches, and likewise are successful given only limited knowledge about the graph.

Recent works show that Graph Neural Networks (GNNs) are highly non-robust with respect to adversarial attacks on both the graph structure and the node attributes, making their outcomes unreliable. We propose the first method for certifiable (non-)robustness of graph convolutional networks with respect to perturbations of the node attributes. We consider the case of binary node attributes (e.g. bag-of-words) and perturbations that are L_0-bounded. If a node has been certified with our method, it is guaranteed to be robust under any possible perturbation given the attack model. Likewise, we can certify non-robustness. Finally, we propose a robust semi-supervised training procedure that treats the labeled and unlabeled nodes jointly. As shown in our experimental evaluation, our method significantly improves the robustness of the GNN with only minimal effect on the predictive accuracy.

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks on both the graph structure and the node attributes. We propose the first method for verifying certifiable (non-)robustness to graph perturbations for a general class of models that includes graph neural networks and label/feature propagation. By exploiting connections to PageRank and Markov decision processes our certificates can be efficiently (and under many threat models exactly) computed. Furthermore, we investigate robust training procedures that increase the number of certifiably robust nodes while maintaining or improving the clean predictive accuracy.

Asynchronous event sequences are the basis of many applications throughout different industries. In this work, we tackle the task of predicting the next event (given a history), and how this prediction changes with the passage of time. Since at some time points (e.g. predictions far into the future) we might not be able to predict anything with confidence, capturing uncertainty in the predictions is crucial. We present two new architectures, WGP-LN and FD-Dir, modelling the evolution of the distribution on the probability simplex with time-dependent logistic normal and Dirichlet distributions. In both cases, the combination of RNNs with either Gaussian process or function decomposition allows to express rich temporal evolution of the distribution parameters, and naturally captures uncertainty. Experiments on class prediction, time prediction and anomaly detection demonstrate the high performances of our models on various datasets compared to other approaches.

Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a powerful, yet spatially localized graph convolution: Graph diffusion convolution (GDC). GDC leverages generalized graph diffusion, examples of which are the heat kernel and personalized PageRank. It alleviates the problem of noisy and often arbitrarily defined edges in real graphs. We show that GDC is closely related to spectral-based models and thus combines the strengths of both spatial (message passing) and spectral methods. We demonstrate that replacing message passing with graph diffusion convolution consistently leads to significant performance improvements across a wide range of models on both supervised and unsupervised tasks and a variety of datasets. Furthermore, GDC is not limited to GNNs but can trivially be combined with any graph-based model or algorithm (e.g. spectral clustering) without requiring any changes to the latter or affecting its computational complexity. Our implementation is available online.

We might hope that when faced with unexpected inputs, well-designed software systems would fire off warnings. Machine learning (ML) systems, however, which depend strongly on properties of their inputs (e.g. the i.i.d. assumption), tend to fail silently. This paper explores the problem of building ML systems that fail loudly, investigating methods for detecting dataset shift, identifying exemplars that most typify the shift, and quantifying shift malignancy. We focus on several datasets and various perturbations to both covariates and label distributions with varying magnitudes and fractions of data affected. Interestingly, we show that across the dataset shifts that we explore, a two-sample-testing-based approach, using pre-trained classifiers for dimensionality reduction, performs best. Moreover, we demonstrate that domain-discriminating approaches tend to be helpful for characterizing shifts qualitatively and determining if they are harmful.

Social influence plays a vital role in shaping a user's behavior in online communities dealing with items of fine taste like movies, food, and beer. For online recommendation, this implies that users' preferences and ratings are influenced due to other individuals. Given only time-stamped reviews of users, can we find out who-influences-whom, and characteristics of the underlying influence network? Can we use this network to improve recommendation?

We study the problem of robust attributed graph clustering. In real data, the clustering structure is often obfuscated due to anomalies or corruptions. While robust methods have been recently introduced that handle anomalies as part of the clustering process, they all fail to account for one core aspect: Since attributed graphs consist of two views (network structure and attributes) anomalies might materialize only partially, i.e. instances might be corrupted in one view but perfectly fit in the other. In this case, we can still derive meaningful cluster assignments. Existing works only consider complete anomalies. In this paper, we present a novel probabilistic generative model (PAICAN) that explicitly models partial anomalies by generalizing ideas of Degree Corrected Stochastic Block Models and Bernoulli Mixture Models. We provide a highly scalable variational inference approach with runtime complexity linear in the number of edges. The robustness of our model w.r.t. anomalies is demonstrated by our experimental study, outperforming state-of-the-art competitors.

We propose NetGAN - the first implicit generative model for graphs able to mimic real-world networks. We pose the problem of graph generation as learning the distribution of biased random walks over the input graph. The proposed model is based on a stochastic neural network that generates discrete output samples and is trained using the Wasserstein GAN objective. NetGAN is able to produce graphs that exhibit well-known network patterns without explicitly specifying them in the model definition. At the same time, our model exhibits strong generalization properties, as highlighted by its competitive link prediction performance, despite not being trained specifically for this task. Being the first approach to combine both of these desirable properties, NetGAN opens exciting avenues for further research.

Deep learning models for graphs have achieved strong performance for the task of node classification. Despite their proliferation, currently there is no study of their robustness to adversarial attacks. Yet, in domains where they are likely to be used, e.g. the web, adversaries are common. Can deep learning models for graphs be easily fooled? In this work, we introduce the first study of adversarial attacks on attributed graphs, specifically focusing on models exploiting ideas of graph convolutions. In addition to attacks at test time, we tackle the more challenging class of poisoning/causative attacks, which focus on the training phase of a machine learning model.We generate adversarial perturbations targeting the node's features and the graph structure, thus, taking the dependencies between instances in account. Moreover, we ensure that the perturbations remain unnoticeable by preserving important data characteristics. To cope with the underlying discrete domain we propose an efficient algorithm Nettack exploiting incremental computations. Our experimental study shows that accuracy of node classification significantly drops even when performing only few perturbations. Even more, our attacks are transferable: the learned attacks generalize to other state-of-the-art node classification models and unsupervised approaches, and likewise are successful even when only limited knowledge about the graph is given.

Density estimation is one of the most frequently used data analytics techniques. A major challenge of real-world datasets is missing values, originating e.g. from sampling errors or data loss. The recovery of these is often impossible or too expensive. Missing values are not necessarily limited to a few features or samples, rendering methods based on complete auxiliary variables unsuitable. In this paper we introduce three models able to deal with such datasets. They are based on the new concept of virtual objects. Additionally, we present a computationally efficient approximation. Generalizing KDE, our methods are called Warp-KDE. Experiments with incomplete datasets show that Warp-KDE methods are superior to established imputation methods.

Recently, innovative techniques for text processing like Latent Dirichlet Allocation (LDA) and embedding algorithms like Paragraph Vectors (PV) allowed for improved text classification and retrieval methods. Even though these methods can be adjusted to handle different text collections, they do not take advantage of the fixed document structure that is mandatory in many application areas. In this paper, we focus on patent data which mandates a fixed structure. We propose a new classification method which represents documents as Fixed Hierarchy Vectors (FHV), reflecting the document's structure. FHVs represent a document on multiple levels where each level represents the complete document but with a different local context. Furthermore, we sequentialize this representation and classify documents using LSTM-based architectures. Our experiments show that FHVs provide a richer document representation and that sequential classification improves classification performance when classifying patents into the International Patent Classification (IPC) taxonomy.

Spectral clustering is one of the most prominent clustering approaches. However, it is highly sensitive to noisy input data. In this work, we propose a robust spectral clustering technique able to handle such scenarios. To achieve this goal, we propose a sparse and latent decomposition of the similarity graph used in spectral clustering. In our model, we jointly learn the spectral embedding as well as the corrupted data - thus, enhancing the clustering performance overall. We propose algorithmic solutions to all three established variants of spectral clustering, each showing linear complexity in the number of edges. Our experimental analysis confirms the significant potential of our approach for robust spectral clustering. Supplementary material is available at www.kdd.in.tum.de/RSC.

Given a friendship network, how certain are we that Smith is a progressive (vs. conservative)? How can we propagate these certainties through the network? While Belief propagation marked the beginning of principled label-propagation to classify nodes in a graph, its numerous variants proposed in the literature fail to take into account uncertainty during the propagation process. As we show, this limitation leads to counter-intuitive results for even simple graphs. Motivated by these observations, we formalize axioms that any node classification algorithm should obey and propose NetConf which satisfies these axioms and handles arbitrary network effects (homophily/heterophily) at scale. Our contributions are: (1) Axioms: We state axioms that any node classification algorithm should satisfy; (2) Theory: NetConf is grounded in a Bayesian-theoretic framework to model uncertainties, has a closed-form solution and comes with precise convergence guarantees; (3) Practice: Our method is easy to implement and scales linearly with the number of edges in the graph. On experiments using real world data, we always match or outperform BP while taking less processing time.

Given a heterogeneous network, with nodes of different types - e.g., products, users and sellers from an online recommendation site like Amazon - and labels for a few nodes ('honest', 'suspicious', etc), can we find a closed formula for Belief Propagation (BP), exact or approximate? Can we say whether it will converge? BP, traditionally an inference algorithm for graphical models, exploits so-called "network effects" to perform graph classification tasks when labels for a subset of nodes are provided; and it has been successful in numerous settings like fraudulent entity detection in online retailers and classification in social networks. However, it does not have a closed-form nor does it provide convergence guarantees in general. We propose ZooBP, a method to perform fast BP on undirected heterogeneous graphs with provable convergence guarantees. ZooBP has the following advantages: (1) Generality : It works on heterogeneous graphs with multiple types of nodes and edges; (2) Closed-form solution: ZooBP gives a closed-form solution as well as convergence guarantees; (3) Scalability: ZooBP is linear on the graph size and is up to 600× faster than BP, running on graphs with 3.3 million edges in a few seconds. (4) Effectiveness: Applied on real data (a F lipkart e-commerce network with users, products and sellers), ZooBP identifies fraudulent users with a near-perfect precision of 92.3 % over the top 300 results.

Analytical graph algorithms commonly compute metrics for a graph at one point in time. In practice it is often also of interest how metrics change over time, e.g., to find trends. For this purpose, algorithms must be executed for multiple graph snapshots. We present Single Algorithm Multiple Snapshots (SAMS) , a novel approach to execute algorithms concurrently for multiple graph snapshots. SAMS automatically transforms graph algorithms to leverage similarities between the analyzed graph snapshots. The automatic transformation interleaves algorithm executions on multiple snapshots, synergistically shares their graph accesses and traversals, and optimizes the algorithm's data layout. Thus, SAMS can amortize the cost of random data accesses and improve memory bandwidth utilization---two main cost factors in graph analytics. We extensively evaluate SAMS using six well-known algorithms and multiple synthetic as well as real-world graph datasets. Our measurements show that in multi-snapshot analyses, SAMS offers runtime improvements of up to two orders of magnitude over traditional snapshot-at-a-time execution.

Cliques are frequently used to model communities: a community is a set of nodes where each pair is equally likely to be connected. But studying real-world communities reveals that they have more structure than that. In particular, the nodes can be ordered in such a way that (almost) all edges in the community lie below a hyperbola. In this paper we present three new models for communities that capture this phenomenon. Our models explain the structure of the communities differently, but we also prove that they are identical in their expressive power. Our models fit to real-world data much better than traditional block models or previously-proposed hyperbolic models, both of which are a special case of our model. Our models also allow for intuitive interpretation of the parameters, enabling us to summarize the shapes of the communities in graphs effectively.

Online review communities are dynamic as users join and leave, adopt new vocabulary, and adapt to evolving trends. Recent work has shown that recommender systems benefit from explicit consideration of user experience. However, prior work assumes a fixed number of discrete experience levels, whereas in reality users gain experience and mature continuously over time. This paper presents a new model that captures the continuous evolution of user experience, and the resulting language model in reviews and other posts. Our model is unsupervised and combines principles of Geometric Brownian Motion, Brownian Motion, and Latent Dirichlet Allocation to trace a smooth temporal progression of user experience and language model respectively. We develop practical algorithms for estimating the model parameters from data and for inference with our model (e.g., to recommend items). Extensive experiments with five real-world datasets show that our model not only fits data better than discrete-model baselines, but also outperforms state-of-the-art methods for predicting item ratings.

Review fraud is a pervasive problem in online commerce, in which fraudulent sellers write or purchase fake reviews to manipulate perception of their products and services. Fake reviews are often detected based on several signs, including 1) they occur in short bursts of time; 2) fraudulent user accounts have skewed rating distributions. However, these may both be true in any given dataset. Hence, in this paper, we propose an approach for detecting fraudulent reviews which combines these 2 approaches in a principled manner, allowing successful detection even when one of these signs is not present. To combine these 2 approaches, we formulate our Bayesian Inference for Rating Data (BIRD) model, a flexible Bayesian model of user rating behavior. Based on our model we formulate a likelihood-based suspiciousness metric, Normalized Expected Surprise Total (NEST). We propose a linear-time algorithm for performing Bayesian inference using our model and computing the metric. Experiments on real data show that BIRDNEST successfully spots review fraud in large, real-world graphs: the 50 most suspicious users of the Flipkart platform flagged by our algorithm were investigated and all identified as fraudulent by domain experts at Flipkart.

Preferential attachment models for random graphs are successful in capturing many characteristics of real networks such as power law behavior. At the same time they lack flexibility to take vertex to vertex affinities into account, a feature that is commonly used in many link recommendation algorithms. We propose a random graph model based on both node attributes and preferential attachment. This approach overcomes the limitation of existing models on expressing vertex affinity and on reflecting properties of different subgraphs. We analytically prove that our model preserves the power law behavior in the degree distribution as expressed by natural graphs and we show that it satisfies the small world property. Experiments show that our model provides an excellent fit of many natural graph statistics and we provide an algorithm to infer the associated affinity function efficiently.

Given a large bipartite graph that represents objects and their properties, how can we automatically extract semantic information that provides an overview of the data and -- at the same time -- enables us to drill down to specific parts for an in-depth analysis? In this work, we propose extracting a taxonomy that models the relation between the properties via an is a hierarchy. The extracted taxonomy arranges the properties from general to specific providing different levels of abstraction. Our proposed method has the following desirable properties: (a) it requires no user-defined parameters, by exploiting the principle of minimum description length, (b) it is effective, by utilizing the inheritance of objects when representing the hierarchy, and (c) it is scalable, being linear in the number of edges. We demonstrate the effectiveness and scalability of our method on a broad spectrum of real, publicly available graphs from drug-property graphs to social networks with up to 22 million vertices and 286 million edges.

How can we tell when accounts are fake or real in a social network? And how can we tell which accounts belong to liberal, conservative or centrist users? Often, we can answer such questions and label nodes in a network based on the labels of their neighbors and appropriate assumptions of homophily ("birds of a feather flock together") or heterophily ("opposites attract"). One of the most widely used methods for this kind of inference is Belief Propagation (BP) which iteratively propagates the information from a few nodes with explicit labels throughout a network until convergence. A well-known problem with BP, however, is that there are no known exact guarantees of convergence in graphs with loops. This paper introduces Linearized Belief Propagation (LinBP), a linearization of BP that allows a closed-form solution via intuitive matrix equations and, thus, comes with exact convergence guarantees. It handles homophily, heterophily, and more general cases that arise in multi-class settings. Plus, it allows a compact implementation in SQL. The paper also introduces Single-pass Belief Propagation (SBP), a localized (or "myopic") version of LinBP that propagates information across every edge at most once and for which the final class assignments depend only on the nearest labeled neighbors. In addition, SBP allows fast incremental updates in dynamic networks. Our runtime experiments show that LinBP and SBP are orders of magnitude faster than standard BP, while leading to almost identical node labels.

Since data is often multi-faceted in its very nature, it might not adequately be summarized by just a single clustering. To better capture the data's complexity, methods aiming at the detection of multiple, alternative clusterings have been proposed. Independent of this research area, semi-supervised clustering techniques have shown to substantially improve clustering results for single-view clustering by integrating prior knowledge. In this paper, we join both research areas and present a solution for integrating prior knowledge in the process of detecting multiple clusterings.

Rating data is ubiquitous on websites such as Amazon, TripAdvisor, or Yelp. Since ratings are not static but given at various points in time, a temporal analysis of rating data provides deeper insights into the evolution of a product's quality. In this work, we tackle the following question: Given the time stamped rating data for a product or service, how can we detect the general rating behavior of users as well as time intervals where the ratings behave anomalous? We propose a Bayesian model that represents the rating data as sequence of categorical mixture models. In contrast to existing methods, our method does not require any aggregation of the input but it operates on the original time stamped data. To capture the dynamic effects of the ratings, the categorical mixtures are temporally constrained: Anomalies can occur in specific time intervals only and the general rating behavior should evolve smoothly over time. Our method automatically determines the intervals where anomalies occur, and it captures the temporal effects of the general behavior by using a state space model on the natural parameters of the categorical distributions. For learning our model, we propose an efficient algorithm combining principles from variational inference and dynamic programming. In our experimental study we show the effectiveness of our method and we present interesting discoveries on multiple real world datasets.

User provided rating data about products and services is one key feature of websites such as Amazon, TripAdvisor, or Yelp. Since these ratings are rather static but might change over time, a temporal analysis of rating distributions provides deeper insights into the evolution of a products' quality. Given a time-series of rating distributions, in this work, we answer the following questions: (1) How to detect the base behavior of users regarding a product's evaluation over time? (2) How to detect points in time where the rating distribution differs from this base behavior, e.g., due to attacks or spontaneous changes in the product's quality? To achieve these goals, we model the base behavior of users regarding a product as a latent multivariate autoregressive process. This latent behavior is mixed with a sparse anomaly signal finally leading to the observed data. We propose an efficient algorithm solving our objective and we present interesting findings on various real world datasets.

Clustering is one of the fundamental data mining tasks. While traditional clustering techniques assign each object to a single cluster only, in many applications it has been observed that objects might belong to multiple clusters with different degrees. In this work, we present a Bayesian framework to tackle the challenge of mixed membership clustering for vector data. We exploit the ideas of subspace clustering where the relevance of dimensions might be different for each cluster. Combining the relevance of the dimensions with the cluster membership degree of the objects, we propose a novel type of mixture model able to represent data containing mixed membership subspace clusters. For learning our model, we develop an efficient algorithm based on variational inference allowing easy parallelization. In our empirical study on synthetic and real data we show the strengths of our novel clustering technique.

Clustering graphs annotated with feature vectors has recently gained much attention. The goal is to detect groups of vertices that are densely connected in the graph as well as similar with respect to their feature values. While early approaches treated all dimensions of the feature space as equally important, more advanced techniques consider the varying relevance of dimensions for different groups. In this work, we propose a novel clustering method for graphs with feature vectors based on the principle of spectral clustering. Following the idea of subspace clustering, our method detects for each cluster an individual set of relevant features. Since spectral clustering is based on the eigendecomposition of the affinity matrix, which strongly depends on the choice of features, our method simultaneously learns the grouping of vertices and the affinity matrix. To tackle the fundamental challenge of comparing the clustering structures for different feature subsets, we define an objective function that is unbiased regarding the number of relevant features. We develop the algorithm SSCG and we show its application for multiple real-world datasets.

Detecting dense subgraphs in a large graph is an important graph mining problem and various approaches have been proposed for its solution. While most existing methods only consider unlabeled and one-dimensional graph data, many real-world applications provide far richer information. Thus, in our work, we consider graphs that contain different types of edges -- represented as different layers/dimensions of a graph -- as well as edge labels that further characterize the relations between two vertices. We argue that exploiting this additional information supports the detection of more interesting clusters. In general, we aim at detecting clusters of vertices that are densely connected by edges with similar labels in subsets of the graph layers.

Cluster tracing algorithms are used to mine temporal evolutions of clusters. Generally, clusters represent groups of objects with similar values. In a temporal context like tracing, similar values correspond to similar behavior in one snapshot in time. Recently, tracing based on object-value-similarity was introduced. In this new paradigm, the decision whether two clusters are considered similar is based on the similarity of the clusters' object values. Existing approaches of this paradigm, however, have a severe limitation. The mapping of clusters between snapshots in time is performed pairwise, i.e. global connections between a temporal snapshot's clusters are ignored; thus, impacts of other clusters that may affect the mapping are not considered and incorrect cluster tracings may be obtained.

Data sources representing social networks with additional attribute information about the nodes are widely available in today's applications. Recently, combined clustering methods were introduced that consider graph information and attribute information simultaneously to detect meaningful clusters in such networks. In many cases, such attributed graphs also evolve over time. Therefore, there is a need for clustering methods that are able to trace clusters over different time steps and analyze their evolution over time. In this paper, we extend our combined clustering method DB-CSC to the analysis of evolving combined clusters.

Traditional clustering algorithms identify just a single clustering of the data. Today's complex data, however, allow multiple interpretations leading to several valid groupings hidden in different views of the database. Each of these multiple clustering solutions is valuable and interesting as different perspectives on the same data and several meaningful groupings for each object are given. Especially for high dimensional data, where each object is described by multiple attributes, alternative clusters in different attribute subsets are of major interest. In this tutorial, we describe several real world application scenarios for multiple clustering solutions. We abstract from these scenarios and provide the general challenges in this emerging research area. We describe state-of-the-art paradigms, we highlight specific techniques, and we give an overview of this topic by providing a taxonomy of the existing clustering methods. By focusing on open challenges, we try to attract young researchers for participating in this emerging research field.

Assessing the significance of data mining results is an important step in the knowledge discovery process. While results might appear interesting at a first glance, they can often be explained by already known characteristics of the data. Randomization is an established technique for significance testing, and methods to assess data mining results on vector data or network data have been proposed. In many applications, however, both sources are simultaneously given. Since these sources are rarely independent of each other but highly correlated, naively applying existing randomization methods on each source separately is questionable. In this work, we present a method to assess the significance of mining results on graphs with binary features vectors. We propose a novel null model that preserves correlation information between both sources. Our randomization exploits an adaptive Metropolis sampling and interweaves attribute randomization and graph randomization steps. In thorough experiments, we demonstrate the application of our technique. Our results indicate that while simultaneously using both sources is beneficial, often one source of information is dominant for determining the mining results.

Mining temporal multivariate data by clustering is an important research topic. In today's complex data, interesting patterns are often neither bound to the whole dimensional nor temporal extent of the data domain. This challenge is met by temporal subspace clustering methods. Their effectiveness, however, is impeded by aspects unavoidable in real world data: Misalignments between time series, for example caused by out-of-sync sensors, and measurement errors. Under these conditions, existing temporal subspace clustering approaches miss the patterns contained in the data. In this paper, we propose a novel clustering method that mines temporal subspace clusters reflected by sets of objects and relevant intervals. We enable flexible handling of misaligned time series by adaptively shifting time series in the time domain, and we achieve robustness to measurement errors by allowing certain fractions of deviating values in each relevant point in time. We show the effectiveness of our method in experiments on real and synthetic data.

Mining dense subgraphs such as cliques or quasi-cliques is an important graph mining problem and closely related to the notion of graph clustering. In various applications, graphs are enriched by additional information. For example, we can observe graphs representing different types of relations between the vertices. These multiple edge types can also be viewed as different "layers" of the same graph, which is denoted as a "multi-layer graph" in this work. Additionally, each edge might be annotated by a label characterizing the given relation in more detail. By exploiting all these different kinds of information, the detection of more interesting clusters in the graph can be supported.

Detecting multiple clustering solutions is an emerging research field. While data is often multi-faceted in its very nature, traditional clustering methods are restricted to find just a single grouping. To overcome this limitation, methods aiming at the detection of alternative and multiple clustering solutions have been proposed. In this work, we present a Bayesian framework to tackle the problem of multi-view clustering. We provide multiple generalizations of the data by using multiple mixture models. Each mixture describes a specific view on the data by using a mixture of Beta distributions in subspace projections. Since a mixture summarizes the clusters located in similar subspace projections, each view highlights specific aspects of the data. In addition, our model handles overlapping views, where the mixture components compete against each other in the data generation process. For efficiently learning the distributions, we propose the algorithm MVGen that exploits the ICM principle and uses Bayesian model selection to trade-off the cluster model's complexity against its goodness of fit. With experiments on various real-world data sets, we demonstrate the high potential of MVGen to detect multiple, overlapping clustering views in subspace projections of the data.

The necessity to analyze subspace projections of complex data is a well-known fact in the clustering community. While the full space may be obfuscated by overlapping patterns and irrelevant dimensions, only certain subspaces are able to reveal the clustering structure. Subspace clustering discards irrelevant dimensions and allows objects to belong to multiple, overlapping clusters due to individual subspace projections for each set of objects. As we will demonstrate, the observations, which originate the need to consider subspace projections for traditional clustering, also apply for the task of correlation analysis.

Analysis of temporal climate data is an active research area. Advanced data mining methods designed especially for these temporal data support the domain expert’s pursuit to understand phenomena as the climate change, which is crucial for a sustainable world. Important solutions for mining temporal data are cluster tracing approaches, which are used to mine temporal evolutions of clusters. Generally, clusters represent groups of objects with similar values. In a temporal context like tracing, similar values correspond to similar behavior in one snapshot in time. Each cluster can be interpreted as a behavior type and cluster tracing corresponds to tracking similar behaviors over time. Existing tracing approaches are for datasets satisfying two specific conditions: The clusters appear in all attributes, i.e., fullspace clusters , and the data objects have unique identifiers. These identifiers are used for tracking clusters by measuring the number of objects two clusters have in common, i.e. clusters are traced based on similar object sets . These conditions, however, are strict: First, in complex data, clusters are often hidden in individual subsets of the dimensions . Second, mapping clusters based on similar objects sets does not reflect the idea of tracing similar behavior types over time, because similar behavior can even be represented by clusters having no objects in common. A tracing method based on similar object values is needed. In this paper, we introduce a novel approach that traces subspace clusters based on object value similarity . Neither subspace tracing nor tracing by object value similarity has been done before.

Knowledge discovery in databases requires not only development of novel mining techniques but also fair and comparable quality assessment based on objective evaluation measures. Especially in young research areas where no common measures are available, researchers are unable to provide a fair evaluation. Typically, publications glorify the high quality of one approach only justified by an arbitrary evaluation measure. However, such conclusions can only be drawn if the evaluation measures themselves are fully understood. In this paper, we provide the basis for systematic evaluation in the emerging research area of subspace clustering. We formalize general quality criteria for subspace clustering measures not yet addressed in the literature. We compare the existing external evaluation methods based on these criteria and pinpoint limitations. We propose a novel external evaluation measure which meets the requirements in form of quality properties. In thorough experiments we empirically show characteristic properties of evaluation measures. Overall, we provide a set of evaluation measures that fulfill the general quality criteria as recommendation for future evaluations. All measures and datasets are provided on our website and are integrated in our evaluation framework.

For knowledge discovery in high dimensional databases, subspace clustering detects clusters in arbitrary subspace projections. Scalability is a crucial issue, as the number of possible projections is exponential in the number of dimensions. We propose a scalable density-based subspace clustering method that steers mining to few selected subspace clusters. Our novel steering technique reduces subspace processing by identifying and clustering promising subspaces and their combinations directly. Thereby, it narrows down the search space while maintaining accuracy. Thorough experiments on real and synthetic databases show that steering is efficient and scalable, with high quality results. For future work, our steering paradigm for density-based subspace clustering opens research potential for speeding up other subspace clustering approaches as well.

Fast similarity search in high dimensional feature spaces is crucial in today's applications. Since the performance of traditional index structures degrades with increasing dimensionality, concepts were developed to cope with this curse of dimensionality. Most of the existing concepts exploit global correlations between dimensions to reduce the dimensionality of the feature space. In high dimensional data, however, correlations are often locally constrained to a subset of the data and every object can participate in several of these correlations. Accordingly, discarding the same set of dimensions for each object based on global correlations and ignoring the different correlations of single objects leads to significant loss of information. These aspects are relevant due to the direct correspondence between the degree of information preserved and the achievable query performance.

In today's applications, data analysis tasks are hindered by many attributes per object as well as by faulty data with missing values. Subspace clustering tackles the challenge of many attributes by cluster detection in any subspace projection of the data. However, it poses novel challenges for handling missing values of objects, which are part of multiple subspace clusters in different projections of the data. In this work, we propose a general fault tolerance definition enhancing subspace clustering models to handle missing values. We introduce a flexible notion of fault tolerance that adapts to the individual characteristics of subspace clusters and ensures a robust parameterization. Allowing missing values in our model increases the computational complexity of subspace clustering. Thus, we prove novel monotonicity properties for an efficient computation of fault tolerant subspace clusters. Experiments on real and synthetic data show that our fault tolerance model yields high quality results even in the presence of many missing values. For repeatability, we provide all datasets and executables on our website.

Detecting emerging problems in information and manufacturing systems is the goal of monitoring tools. Good and timely detection of problematic conditions from measured indicators requires efficient and effective detection of critical patterns in a stream of incoming observations.

Today's applications deal with multiple types of information: graph data to represent the relations between objects and attribute data to characterize single objects. Analyzing both data sources simultaneously can increase the quality of mining methods. Recently, combined clustering approaches were introduced, which detect densely connected node sets within one large graph that also show high similarity according to all of their attribute values. However, for attribute data it is known that this full-space clustering often leads to poor clustering results. Thus, subspace clustering was introduced to identify locally relevant subsets of attributes for each cluster. In this work, we propose a method for finding homogeneous groups by joining the paradigms of subspace clustering and dense sub graph mining, i.e. we determine sets of nodes that show high similarity in subsets of their dimensions and that are as well densely connected within the given graph. Our twofold clusters are optimized according to their density, size, and number of relevant dimensions. Our developed redundancy model confines the clustering to a manageable size of only the most interesting clusters. We introduce the algorithm Gamer for the efficient calculation of our clustering. In thorough experiments on synthetic and real world data we show that Gamer achieves low runtimes and high clustering qualities.

Traditional clustering algorithms identify just a single clustering of the data. Today's complex data, however, allow multiple interpretations leading to several valid groupings hidden in different views of the database. Each of these multiple clustering solutions is valuable and interesting as different perspectives on the same data and several meaningful groupings for each object are given. Especially for high dimensional data where each object is described by multiple attributes, alternative clusters in different attribute subsets are of major interest. In this tutorial, we describe several real world application scenarios for multiple clustering solutions. We abstract from these scenarios and provide the general challenges in this emerging research area. We describe state-of-the-art paradigms, we highlight specific techniques, and we give an overview of this topic by providing a taxonomy of the existing methods. By focusing on open challenges, we try to attract young researchers for participating in this emerging research field.

Analyzing uncertain databases is a challenge in data mining research. Usually, data mining methods rely on precise values. In scenarios where uncertain values occur, e.g. due to noisy sensor readings, these algorithms cannot deliver high-quality patterns. Beside uncertainty, data mining methods face another problem: high dimensional data. For finding object groupings with locally relevant dimensions in this data, subspace clustering was introduced. For high dimensional uncertain data, however, deciding whether dimensions are relevant for a subspace cluster is even more challenging; thus, approaches for effective subspace clustering on uncertain databases are needed. In this paper, we develop a method for subspace clustering for uncertain data that delivers high-quality patterns; the information provided by the individual distributions of objects is used in an effective manner. Because in uncertain scenarios a strict assignment of objects to single clusters is not appropriate, we enrich our model with the concept of membership degree. Subspace clustering for uncertain data is computationally expensive; thus, we propose an efficient algorithm. In thorough experiments we show the effectiveness and efficiency of our new subspace clustering method.

Large data resources are ubiquitous in science and business. For these domains, an intuitive view on the data is essential to fully exploit the hidden knowledge. Often, these data can be semantically structured by concepts. Since the determination of concepts requires a thorough analysis of the data, data mining methods have to be applied. In the field of subspace clustering, some techniques have recently shown to be effective for this task. Although these methods generate concept-based patterns, the user has to provide domain knowledge to gain reasonable concepts out of the data. Our demonstration CoDA (Concept Determination and Analysis) is a tool that supports the user in the final step of concept definition. More concretely, the user is guided through an iterative, interactive process in which concepts are suggested, analyzed, and potentially refined. The core aspect of CoDA is an intuitive, concept-driven presentation of subspace clusters such that concepts can be visually captured.

In the knowledge discovery process, clustering is an established technique for grouping objects based on mutual similarity. However, in today's applications for each object very many attributes are provided. As multiple concepts described by different attributes are mixed in the same data set, clusters do not appear in all dimensions. In these high dimensional data spaces, each object can be clustered in several projections of the data. However, recent clustering techniques do not succeed in detection of these orthogonal concepts hidden in the data. They either miss multiple concepts for each object by partitioning approaches or provide redundant clusters in very similar subspaces.

Subspace clustering aims at detecting clusters in any subspace projection of a high dimensional space. As the number of possible subspace projections is exponential in the number of dimensions, the result is often tremendously large. Recent approaches fail to reduce results to relevant subspace clusters. Their results are typically highly redundant, i.e. many clusters are detected multiple times in several projections. In this work, we propose a novel model for relevant subspace clustering (RESCU). We present a global optimization which detects the most interesting non-redundant subspace clusters. We prove that computation of this model is NP-hard. For RESCU, we propose an approximative solution that shows high accuracy with respect to our relevance model. Thorough experiments on synthetic and real world data show that RESCU successfully reduces the result to manageable sizes. It reliably achieves top clustering quality while competing approaches show greatly varying performance.

Subspace clustering and frequent itemset mining via “step-by-step” algorithms that search the subspace/pattern lattice in a top-down or bottom-up fashion do not scale to large high dimensional data bases. Recent “jump” algorithms directly choose candidate subspace regions or patterns. Their scalability and quality depend heavily on the rating of these candidates as mislead jumps incur poor results and costly candidate refinements. Existing techniques rely on simple statistics with low estimation quality or on inefficient data base scans. In this work, we propose DensEst, an efficient density estimator with significantly improved accuracy. It efficiently provides rough estimates of object counts in selective subspace regions. Furthermore, by incorporating correlations between dimensions DensEst achieves not only efficient but also highly accurate estimations. We show how this density estimation technique can be easily integrated into subspace clustering and frequent itemset mining algorithms to improve both their efficiency and accuracy. We demonstrate the performance of our density estimation technique in thorough experiments and show its efficiency and accuracy improvement for existing algorithms.

Clustering high dimensional data is an emerging research field.Subspace clusteringorprojected clusteringgroup similar objects in subspaces, i.e. projections, of the full space. In the past decade, several clustering paradigms have been developed in parallel, without thorough evaluation and comparison between these paradigms on a common basis. Conclusive evaluation and comparison is challenged by three major issues. First, there is no ground truth that describes the "true" clusters in real world data. Second, a large variety of evaluation measures have been used that reflect different aspects of the clustering result. Finally, in typical publications authors have limited their analysis to their favored paradigm only, while paying other paradigms little or no attention. In this paper, we take a systematic approach to evaluate the major paradigms in a common framework. We study representative clustering algorithms to characterize the different aspects of each paradigm and give a detailed comparison of their properties. We provide a benchmark set of results on a large variety of real world and synthetic data sets. Using different evaluation measures, we broaden the scope of the experimental analysis and create a common baseline for future developments and comparable evaluations in the field. For repeatability, all implementations, data sets and evaluation measures are available on our website.