Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize adjacency matrix representations, this work revisits an alternative approach that represents graphs as sequences of node set and edge set. We advocate for this approach due to its efficient encoding of graphs and propose a novel representation. Based on this representation, we introduce the Graph Generative Pre-trained Transformer (G2PT), an auto-regressive model that learns graph structures via next-token prediction. To further exploit G2PT’s capabilities as a general-purpose foundation model, we explore fine-tuning strategies for two downstream applications: goal-oriented generation and graph property prediction. We conduct extensive experiments across multiple datasets. Results indicate that G2PT achieves superior generative performance on both generic graph and molecule datasets. Furthermore, G2PT exhibits strong adaptability and versatility in downstream tasks from molecular design to property prediction.

Neurosymbolic decision-making agents inherit many of the critical transparency and interpretability benefits of planning-based symbolic agents but also face one of their central challenges: the Symbol Grounding Problem (SGP). Grounding hand-crafted symbolic planning domains to percepts typically requires training models with extensive annotated data which hinders their applicability to broader problems. In this work we propose Act-to-Ground (A2G), a framework for training grounding models for symbolic planners with weak supervision obtained through environment interaction or demonstrations. We first cast the grounding problem as an inference problem and 1) use satisfiability-based planning to provide weak supervision to the grounding model by exploiting knowledge already built into the planning domain, 2) propose an MCMC sampler that enables sampling weak labels for grounding planners, 3) improve neurosymbolic grounding performance via a score-matching objective and 4) propose a learnability condition for learning grounding models for planners.

Finding Minimal Unsatisfiable Subsets (MUSes) of boolean constraints is a common problem in infeasibility analysis of over-constrained systems. However, because of the exponential search space of the problem, enumerating MUSes is extremely time-consuming in real applications. In this work, we propose to prune formulas using a learned model to speed up MUS enumeration. We represent formulas as graphs and then develop a graph-based learning model to predict which part of the formula should be pruned. Importantly, the training of our model does not require labeled data. It does not even require training data from the target application because it extrapolates to data with different distributions. In our experiments we combine our model with existing MUS enumerators and validate its effectiveness in multiple benchmarks including a set of real-world problems outside our training distribution. The experiment results show that our method significantly accelerates MUS enumeration on average on these benchmark problems.

The discovery and identification of molecules in biological and environmental samples is crucial for advancing biomedical and chemical sciences. Tandem mass spectrometry (MS/MS) is the leading technique for high-throughput elucidation of molecular structures. However, decoding a molecular structure from its mass spectrum is exceptionally challenging, even when performed by human experts. As a result, the vast majority of acquired MS/MS spectra remain uninterpreted, thereby limiting our understanding of the underlying (bio)chemical processes. Despite decades of progress in machine learning applications for predicting molecular structures from MS/MS spectra, the development of new methods is severely hindered by the lack of standard datasets and evaluation protocols. To address this problem, we propose MassSpecGym -- the first comprehensive benchmark for the discovery and identification of molecules from MS/MS data. Our benchmark comprises the largest publicly available collection of high-quality MS/MS spectra and defines three MS/MS annotation challenges: \textit{de novo} molecular structure generation, molecule retrieval, and spectrum simulation. It includes new evaluation metrics and a generalization-demanding data split, therefore standardizing the MS/MS annotation tasks and rendering the problem accessible to the broad machine learning community. MassSpecGym is publicly available at \url{https://github.com/pluskal-lab/MassSpecGym}.

MOTIVATION: A key challenge in metabolomics is annotating measured spectra from a biological sample with chemical identities. Currently, only a small fraction of measurements can be assigned identities. Two complementary computational approaches have emerged to address the annotation problem: mapping candidate molecules to spectra, and mapping query spectra to molecular candidates. In essence, the candidate molecule with the spectrum that best explains the query spectrum is recommended as the target molecule. Despite candidate ranking being fundamental in both approaches, limited prior works incorporated rank learning tasks in determining the target molecule. RESULTS: We propose a novel machine learning model, Ensemble Spectral Prediction (ESP), for metabolite annotation. ESP takes advantage of prior neural network-based annotation models that utilize multilayer perceptron (MLP) networks and Graph Neural Networks (GNNs). Based on the ranking results of the MLP- and GNN-based models, ESP learns a weighting for the outputs of MLP and GNN spectral predictors to generate a spectral prediction for a query molecule. Importantly, training data is stratified by molecular formula to provide candidate sets during model training. Further, baseline MLP and GNN models are enhanced by considering peak dependencies through label mixing and multi-tasking on spectral topic distributions. When trained on the NIST 2020 dataset and evaluated on the relevant candidate sets from PubChem, ESP improves average rank by 23.7% and 37.2% over the MLP and GNN baselines, respectively, demonstrating performance gain over state-of-the-art neural network approaches. However, MLP approaches remain strong contenders when considering top five ranks. Importantly, we show that annotation performance is dependent on the training dataset, the number of molecules in the candidate set and candidate similarity to the target molecule. AVAILABILITY AND IMPLEMENTATION: The ESP code, a trained model, and a Jupyter notebook that guide users on using the ESP tool is available at https://github.com/HassounLab/ESP.

Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this work, we propose EDGE, a new diffusion-based generative graph model that addresses generative tasks with large graphs. To improve computation efficiency, we encourage graph sparsity by using a discrete diffusion process that randomly removes edges at each time step and finally obtains an empty graph. EDGE only focuses on a portion of nodes in the graph at each denoising step. It makes much fewer edge predictions than previous diffusion-based models. Moreover, EDGE admits explicitly modeling the node degrees of the graphs, further improving the model performance. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by our approach have more similar graph statistics to those of the training graphs.

Data subsampling is widely used to speed up the training of large-scale recommendation systems. Most subsampling methods are model-based and often require a pre-trained pilot model to measure data importance via e.g. sample hardness. However, when the pilot model is misspecified, model-based subsampling methods deteriorate. Since model misspecification is persistent in real recommendation systems, we instead propose model-agnostic data subsampling methods by only exploring input data structure represented by graphs. Specifically, we study the topology of the user-item graph to estimate the importance of each user-item interaction (an edge in the user-item graph) via graph conductance, followed by a propagation step on the network to smooth out the estimated importance value. Since our proposed method is model-agnostic, we can marry the merits of both model-agnostic and model-based subsampling methods. Empirically, we show that combing the two consistently improves over any single method on the used datasets. Experimental results on KuaiRec and MIND datasets demonstrate that our proposed methods achieve superior results compared to baseline approaches.

Self-supervised training methods for transformers have demonstrated remarkable performance across various domains. Previous transformer-based models, such as masked autoencoders (MAE), typically utilize a single normalization layer for both the [CLS] symbol and the tokens. We propose in this paper a simple modification that employs separate normalization layers for the tokens and the [CLS] symbol to better capture their distinct characteristics and enhance downstream task performance. Our method aims to alleviate the potential negative effects of using the same normalization statistics for both token types, which may not be optimally aligned with their individual roles. We empirically show that by utilizing a separate normalization layer, the [CLS] embeddings can better encode the global contextual information and are distributed more uniformly in its anisotropic space. When replacing the conventional normalization layer with the two separate layers, we observe an average 2.7% performance improvement over the image, natural language, and graph domains.

Accurate prediction of dynamical systems in unstructured meshes has recently shown successes in scientific simulations. Many dynamical systems have a nonnegligible level of stochasticity introduced by various factors (e.g. chaoticity), so there is a need for a unified framework that captures both deterministic and stochastic components in the rollouts of these systems. Inspired by regeneration learning, we propose a new model that combines generative and sequential networks to model dynamical systems. Specifically, we use an autoencoder to learn compact representations of full-space physical variables in a low-dimensional space. We then integrate a transformer with a conditional normalizing flow model to model the temporal sequence of latent representations. We evaluate the new model in both deterministic and stochastic systems. The model outperforms several competitive baseline models and makes more accurate predictions of deterministic systems. Its own prediction error is also reflected in its uncertainty estimations. When predicting stochastic systems, the proposed model generates high-quality rollout samples. The mean and variance of these samples well match the statistics of samples computed from expensive numerical simulations.

MOTIVATION: While traditionally utilized for identifying site-specific metabolic activity within a compound to alter its interaction with a metabolizing enzyme, predicting the site-of-metabolism (SOM) is essential in analyzing the promiscuity of enzymes on substrates. The successful prediction of SOMs and the relevant promiscuous products has a wide range of applications that include creating extended metabolic models (EMMs) that account for enzyme promiscuity and the construction of novel heterologous synthesis pathways. There is therefore a need to develop generalized methods that can predict molecular SOMs for a wide range of metabolizing enzymes. RESULTS: This article develops a Graph Neural Network (GNN) model for the classification of an atom (or a bond) being an SOM. Our model, GNN-SOM, is trained on enzymatic interactions, available in the KEGG database, that span all enzyme commission numbers. We demonstrate that GNN-SOM consistently outperforms baseline machine learning models, when trained on all enzymes, on Cytochrome P450 (CYP) enzymes, or on non-CYP enzymes. We showcase the utility of GNN-SOM in prioritizing predicted enzymatic products due to enzyme promiscuity for two biological applications: the construction of EMMs and the construction of synthesis pathways. AVAILABILITY AND IMPLEMENTATION: A python implementation of the trained SOM predictor model can be found at https://github.com/HassounLab/GNN-SOM. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We consider the problem of fitting autoregressive graph generative models via maximum likelihood estimation (MLE). MLE is intractable for graph autoregressive models because the nodes in a graph can be arbitrarily reordered; thus the exact likelihood involves a sum over all possible node orders leading to the same graph. In this work, we fit the graph models by maximizing a variational bound, which is built by first deriving the joint probability over the graph and the node order of the autoregressive process. This approach avoids the need to specify ad-hoc node orders, since an inference network learns the most likely node sequences that have generated a given graph. We improve the approach by developing a graph generative model based on attention mechanisms and an inference network based on routing search. We demonstrate empirically that fitting autoregressive graph models via variational inference improves their qualitative and quantitative performance, and the improved model and inference network further boost the performance.

MOTIVATION: Despite experimental and curation efforts, the extent of enzyme promiscuity on substrates continues to be largely unexplored and under documented. Providing computational tools for the exploration of the enzyme-substrate interaction space can expedite experimentation and benefit applications such as constructing synthesis pathways for novel biomolecules, identifying products of metabolism on ingested compounds, and elucidating xenobiotic metabolism. Recommender systems (RS), which are currently unexplored for the enzyme-substrate interaction prediction problem, can be utilized to provide enzyme recommendations for substrates, and vice versa. The performance of Collaborative-Filtering (CF) RSs; however, hinges on the quality of embedding vectors of users and items (enzymes and substrates in our case). Importantly, enhancing CF embeddings with heterogeneous auxiliary data, specially relational data (e.g. hierarchical, pairwise or groupings), remains a challenge. RESULTS: We propose an innovative general RS framework, termed Boost-RS that enhances RS performance by 'boosting' embedding vectors through auxiliary data. Specifically, Boost-RS is trained and dynamically tuned on multiple relevant auxiliary learning tasks Boost-RS utilizes contrastive learning tasks to exploit relational data. To show the efficacy of Boost-RS for the enzyme-substrate prediction interaction problem, we apply the Boost-RS framework to several baseline CF models. We show that each of our auxiliary tasks boosts learning of the embedding vectors, and that contrastive learning using Boost-RS outperforms attribute concatenation and multi-label learning. We also show that Boost-RS outperforms similarity-based models. Ablation studies and visualization of learned representations highlight the importance of using contrastive learning on some of the auxiliary data in boosting the embedding vectors. AVAILABILITY AND IMPLEMENTATION: A Python implementation for Boost-RS is provided at https://github.com/HassounLab/Boost-RS. The enzyme-substrate interaction data is available from the KEGG database (https://www.genome.jp/kegg/).

When formulated as an unsupervised learning problem, anomaly detection often requires a model to learn the distribution of normal data. Previous works modify Generative Adversarial Networks (GANs) by using encoder-decoders as generators and apply them to anomaly detection tasks. Previous studies indicate that GAN ensembles are often more stable than single GANs in image generation tasks. In this work, we propose to construct GAN ensembles for anomaly detection. In the proposed method, a group of generators interact with a group of discriminators, so every generator gets feedback from every discriminator, and vice versa. Compared to a single GAN, an ensemble of GANs can better model the distribution of normal data and thus better detect anomalies. We also make a theoretical analysis of GANs and GAN ensembles in the context of anomaly detection. The empirical study constructs ensembles based on four different types of detecting models, and the results show that the ensemble outperforms the single model for all four model types.

A graph generative model defines a distribution over graphs. Typically, the model consists of a sequential process that creates and adds nodes and edges. Such sequential process defines an ordering of the nodes in the graph. The computation of the model’s likelihood requires to marginalize the node orderings; this makes maximum likelihood estimation (MLE) challenging due to the (factorial) number of possible permutations. In this work, we provide an expression for the likelihood of a graph generative model and show that its calculation is closely related to the problem of graph automorphism. In addition, we derive a variational inference (VI) algorithm for fitting a graph generative model that is based on the maximization of a variational bound of the log-likelihood. This allows the model to be trained with node orderings from the approximate posterior instead of ad-hoc orderings. Our experiments show that our log-likelihood bound is significantly tighter than the bound of previous schemes. The models fitted with the VI algorithm are able to generate high-quality graphs that match the structures of target graphs not seen during training.

Recent works apply Graph Neural Networks (GNNs) to graph matching tasks and show promising results. Considering that model outputs are complex matchings, we devise several techniques to improve the learning of GNNs and obtain a new model, Stochastic Iterative Graph MAtching (SIGMA). Our model predicts a distribution of matchings, instead of a single matching, for a graph pair so the model can explore several probable matchings. We further introduce a novel multi-step matching procedure, which learns how to refine a graph pair’s matching results incrementally. The model also includes dummy nodes so that the model does not have to find matchings for nodes without correspondence. We fit this model to data via scalable stochastic optimization. We conduct extensive experiments across synthetic graph datasets as well as biochemistry and computer vision applications. Across all tasks, our results show that SIGMA can produce significantly improved graph matching results compared to state-of-the-art models. Ablation studies verify that each of our components (stochastic training, iterative matching, and dummy nodes) offers noticeable improvement.

MOTIVATION: The complete characterization of enzymatic activities between molecules remains incomplete, hindering biological engineering and limiting biological discovery. We develop in this work a technique, enzymatic link prediction (ELP), for predicting the likelihood of an enzymatic transformation between two molecules. ELP models enzymatic reactions cataloged in the KEGG database as a graph. ELP is innovative over prior works in using graph embedding to learn molecular representations that capture not only molecular and enzymatic attributes but also graph connectivity. RESULTS: We explore transductive (test nodes included in the training graph) and inductive (test nodes not part of the training graph) learning models. We show that ELP achieves high AUC when learning node embeddings using both graph connectivity and node attributes. Further, we show that graph embedding improves link prediction by 30% in area under curve over fingerprint-based similarity approaches and by 8% over support vector machines. We compare ELP against rule-based methods. We also evaluate ELP for predicting links in pathway maps and for reconstruction of edges in reaction networks of four common gut microbiota phyla: actinobacteria, bacteroidetes, firmicutes and proteobacteria. To emphasize the importance of graph embedding in the context of biochemical networks, we illustrate how graph embedding can guide visualization. AVAILABILITY AND IMPLEMENTATION: The code and datasets are available through https://github.com/HassounLab/ELP.

Spatial interpolation is a class of estimation problems where locations with known values are used to estimate values at other locations, with an emphasis on harnessing spatial locality and trends. Traditional kriging methods have strong Gaussian assumptions, and as a result, often fail to capture complexities within the data. Inspired by the recent progress of graph neural networks, we introduce Kriging Convolutional Networks (KCN), a method of combining advantages of Graph Neural Networks (GNN) and kriging. Compared to standard GNNs, KCNs make direct use of neighboring observations when generating predictions. KCNs also contain the kriging method as a specific configuration. Empirically, we show that this model outperforms GNNs and kriging in several applications.

The inference of Gaussian Processes concerns the distribution of the underlying function given observed data points. GP inference based on local ranges of data points is able to capture fine-scale correlations and allow fine-grained decomposition of the computation. Following this direction, we propose a new inference model that considers the correlations and observations of the K nearest neighbors for the inference at a data point. Compared with previous works, we also eliminate the data ordering prerequisite to simplify the inference process. Additionally, the inference task is decomposed to small subtasks with several technique innovations, making our model well suits the stochastic optimization. Since the decomposed small subtasks have the same structure, we further speed up the inference procedure with amortized inference. Our model runs efficiently and achieves good performances on several benchmark tasks.

GP Inference on large datasets is computationally expensive, especially when the observation likelihood is non-Gaussian. To reduce the computation, many recent variational inference methods define the variational distribution based on a small number of inducing points. These methods have a hard tradeoff between distribution flexibility and computational efficiency. In this paper, we focus on the approximation of GP posterior at a local level: we define a reusable template to approximate the posterior at neighborhoods while maintaining a global approximation. We first construct a variational distribution such that the inference for a data point considers only its neighborhood, thereby separating the calculation for each data point. We then train Graph Convolutional Networks as a reusable model to run inference for each data point. Comparing to previous methods, our method greatly reduces the number of parameters and also the number of optimization iterations. In empirical evaluations, the proposed method significantly speeds up the inference and often gets more accurate results than competing methods.

Word embeddings are an effective tool to analyze language. They have been recently extended to model other types of data beyond text, such as items in recommendation systems. Embedding models consider the probability of a target observation (a word or an item) conditioned on the elements in the context (other words or items). In this paper, we show that conditioning on all the elements in the context is not optimal. Instead, we model the probability of the target conditioned on a learned subset of the elements in the context. We use amortized variational inference to automatically choose this subset. Compared to standard embedding models, this method improves predictions and the quality of the embeddings.

In the Superset Label Learning (SLL) problem, weak supervision is provided in the form of a \it superset of labels that contains the true label. If the classifier predicts a label outside of the superset, it commits a \it superset error. Most existing SLL algorithms learn a multiclass classifier by minimizing the superset error. However, only limited theoretical analysis has been dedicated to this approach. In this paper, we analyze Empirical Risk Minimizing learners that use the superset error as the empirical risk measure. SLL data can arise either in the form of independent instances or as multiple-instance bags. For both scenarios, we give the conditions for ERM learnability and sample complexity for the realizable case.

The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous work has explored Markov Chain Monte Carlo (MCMC) and MAP approximations for learning and inference. This paper studies Gaussian approximations to the CGM. As the population grows large, we show that the CGM distribution converges to a multivariate Gaussian distribution (GCGM) that maintains the conditional independence properties of the original CGM. If the observations are exact marginals of the CGM or marginals that are corrupted by Gaussian noise, inference in the GCGM approximation can be computed efficiently in closed form. If the observations follow a different noise model (e.g., Poisson), then expectation propagation provides efficient and accurate approximate inference. The accuracy and speed of GCGM inference is compared to the MCMC and MAP methods on a simulated bird migration problem. The GCGM matches or exceeds the accuracy of the MAP method while being significantly faster.

In the superset label learning problem (SLL), each training instance provides a set of candidate labels of which one is the true label of the instance. As in ordinary regression, the candidate label set is a noisy version of the true label. In this work, we solve the problem by maximizing the likelihood of the candidate label sets of training instances. We propose a probabilistic model, the Logistic Stick- Breaking Conditional Multinomial Model (LSB-CMM), to do the job. The LSB- CMM is derived from the logistic stick-breaking process. It first maps data points to mixture components and then assigns to each mixture component a label drawn from a component-specific multinomial distribution. The mixture components can capture underlying structure in the data, which is very useful when the model is weakly supervised. This advantage comes at little cost, since the model introduces few additional parameters. Experimental tests on several real-world problems with superset labels show results that are competitive or superior to the state of the art. The discovered underlying structures also provide improved explanations of the classification predictions.

Outlier detection often works in an unsupervised manner due to the difficulty of obtaining enough training data. Since outliers are rare, one has to label a very large dataset to include enough outliers in the training set, with which classifiers could sufficiently learn the concept of outliers. Labeling a large training set is costly for most applications. However, we could just label suspected instances identified by unsupervised methods. In this way, the number of instances to be labeled could be greatly reduced. Based on this idea, we propose CISO, an algorithm Constructing training set by Identifying Suspected Outliers. In this algorithm, instances in a pool are first ranked by an unsupervised outlier detection algorithm. Then, suspected instances are selected and hand-labeled, and all remaining instances receive label of in-lier. As such, all instances in the pool are labeled and used in the training set. We also propose Budgeted CISO (BCISO), with which user could set a fixed budget for labeling. Experiments show that both algorithms achieve good performance compared to other methods when the same amount of labeling effort are used.

Important ecological phenomena are often observed indirectly. Consequently, probabilistic latent variable models provide an important tool, because they can include explicit models of the ecological phenomenon of interest and the process by which it is observed. However, existing latent variable methods rely on hand-formulated parametric models, which are expensive to design and require extensive preprocessing of the data. Nonparametric methods (such as regression trees) automate these decisions and produce highly accurate models. However, existing tree methods learn direct mappings from inputs to outputs — they cannot be applied to latent variable models. This paper describes a methodology for integrating nonparametric tree methods into probabilistic latent variable models by extending functional gradient boosting. The approach is presented in the context of occupancy-detection (OD) modeling, where the goal is to model the distribution of a species from imperfect detections. Experiments on 12 real and 3 synthetic bird species compare standard and tree-boosted OD models (latent variable models) with standard and tree-boosted logistic regression models (without latent structure). All methods perform similarly when predicting the observed variables, but the OD models learn better representations of the latent process. Most importantly, tree-boosted OD models learn the best latent representations when nonlinearities and interactions are present.

Linear discriminant analysis (LDA) is a well-known dimension reduction approach, which projects high-dimensional data into a low-dimensional space with the best separation of different classes. In many tasks, the data accumulates over time, and thus incremental LDA is more desirable than batch LDA. Several incremental LDA algorithms have been developed and achieved success; however, the eigen-problem involved requires a large computation cost, which hampers the efficiency of these algorithms. In this paper, we propose a new incremental LDA algorithm, LS-ILDA, based on the least square solution of LDA. When new samples are received, LS-ILDA incrementally updates the least square solution of LDA. Our analysis discloses that this algorithm produces the exact least square solution of batch LDA, while its computational cost is O(min(n, d) × d) for one update on dataset containing n instances in d-dimensional space. Experimental results show that comparing with state-of-the-art incremental LDA algorithms, our proposed LS-ILDA achieves high accuracy with low time cost.

With the rapid evolution of Internet applications, people all over the world are sharing pictures, videos and audios online, and thus, content-based analysis is often demanded. Test efficiency is crucial to the success of online information processing. One obstacle to high-speed testing is the time cost of feature extraction for test objects, particularly for objects with complex representation such as images, videos and audios. In this paper, we study the problem of reducing test time cost by extracting cheap but sufficient features. We propose the TEFE (time-efficient feature extraction) approach, which balances between the test accuracy and test time cost by extracting a proper subset of features for each test object. In the implementation, TEFE trains a sequence of support vector machines and classifies each test object cascadingly. Empirical study shows that TEFE is time efficient while holding a classification accuracy close to that of using all features. It also shows that the test time is linearly adjustable in TEFE.