This work investigates an important phenomenon in centroid-based deep clustering (DC) algorithms: Performance quickly saturates after a period of rapid early gains. Practitioners commonly address early saturation with periodic reclustering, which we demonstrate to be insufficient to address performance plateaus. We call this phenomenon the “reclustering barrier” and empirically show when the reclustering barrier occurs, what its underlying mechanisms are, and how it is possible to Break the Reclustering Barrier with our algorithm BRB. BRB avoids early over-commitment to initial clusterings and enables continuous adaptation to reinitialized clustering targets while remaining conceptually simple. Applying our algorithm to widely-used centroid-based DC algorithms, we show that (1) BRB consistently improves performance across a wide range of clustering benchmarks, (2) BRB enables training from scratch, and (3) BRB performs competitively against state-of-the-art DC algorithms when combined with a contrastive loss. We release our code and pre-trained models at https://github.com/Probabilistic-and-Interactive-ML/breaking-the-reclustering-barrier .

We consider the challenging problem of using domain knowledge to improve deep reinforcement learning policies. To this end, we propose LEGIBLE, a novel approach, following a multi-step process, which starts by mining rules from a deep RL policy, constituting a partially symbolic representation. These rules describe which decisions the RL policy makes and which it avoids making. In the second step, we generalize the mined rules using domain knowledge expressed as metamorphic relations. We adapt these relations from software testing to RL to specify expected changes of actions in response to changes in observations. The third step is evaluating generalized rules to determine which generalizations improve performance when enforced. These improvements show weaknesses in the policy, where it has not learned the general rules and thus can be improved by rule guidance. LEGIBLE supported by metamorphic relations provides a principled way of expressing and enforcing domain knowledge about RL environments. We show the efficacy of our approach by demonstrating that it effectively finds weaknesses, accompanied by explanations of these weaknesses, in eleven RL environments and by showcasing that guiding policy execution with rules improves performance w.r.t. gained reward.

Although there exist instance-dependent regret bounds for linear Markov decision processes (MDPs) and low-rank bandits, extensions to low-rank MDPs remain unexplored. In this work, we close this gap and provide regret bounds for low-rank MDPs in an instance-dependent setting. Specifically, we introduce an algorithm, called UniSREP-UCB, which utilizes a constrained optimization objective to learn features with good spectral properties. Furthermore, we demonstrate that our algorithm enjoys constant regret if the minimal sub-optimality gap and the occupancy distribution of the optimal policy are well-defined and known. To the best of our knowledge, these are the first instance-dependent regret results for low-rank MDPs.

Every AI system that makes decisions about people has a group of stakeholders that are personally affected by these decisions. However, explanations of AI systems rarely address the information needs of this stakeholder group, who often are AI novices. This creates a gap between conveyed information and information that matters to those who are impacted by the system’s decisions, such as domain experts and decision subjects. To address this, we present the “XAI Novice Question Bank”, an extension of the XAI Question Bank (Liao et al., 2020) containing a catalog of information needs from AI novices in two use cases: employment prediction and health monitoring. The catalog covers the categories of data, system context, system usage, and system specifications. We gathered information needs through task based interviews where participants asked questions about two AI systems to decide on their adoption and received verbal explanations in response. Our analysis showed that participants’ confidence increased after receiving explanations but that their understanding faced challenges. These included difficulties in locating information and in assessing their own understanding, as well as attempts to outsource understanding. Additionally, participants’ prior perceptions of the systems’ risks and benefits influenced their information needs. Participants who perceived high risks sought explanations about the intentions behind a system’s deployment, while those who perceived low risks rather asked about the system’s operation. Our work aims to support the inclusion of AI novices in explainability efforts by highlighting their information needs, aims, and challenges. We summarize our findings as five key implications that can inform the design of future explanations for lay stakeholder audiences. • People affected by algorithmic systems should be better considered in explainable AI. • Their interests lie in a system’s context and usage rather than in technical details. • Explanations must meet their information needs in order to support their agency. • Leveraging cognitive processes could improve the understandability of explanations. • Affected people’s perceptions of risks and benefits impact their information needs.

We propose Convex Constraint Learning for Reinforcement Learning (CoCoRL), a novel approach for inferring shared constraints in a Constrained Markov Decision Process (CMDP) from a set of safe demonstrations with possibly different reward functions. While previous work is limited to demonstrations with known rewards or fully known environment dynamics, CoCoRL can learn constraints from demonstrations with different unknown rewards without knowledge of the environment dynamics. CoCoRL constructs a convex safe set based on demonstrations, which provably guarantees safety even for potentially sub-optimal (but safe) demonstrations. For near-optimal demonstrations, CoCoRL converges to the true safe set with no policy regret. We evaluate CoCoRL in gridworld environments and a driving simulation with multiple constraints. CoCoRL learns constraints that lead to safe driving behavior. Importantly, we can safely transfer the learned constraints to different tasks and environments. In contrast, alternative methods based on Inverse Reinforcement Learning (IRL) often exhibit poor performance and learn unsafe policies.

While machine learning is traditionally a resource intensive task, embedded systems, autonomous navigation, and the vision of the Internet of Things fuel the interest in resource-efficient approaches. These approaches aim for a carefully chosen trade-off between performance and resource consumption in terms of computation and energy. The development of such approaches is among the major challenges in current machine learning research and key to ensure a smooth transition of machine learning technology from a scientific environment with virtually unlimited computing resources into everyday's applications. In this article, we provide an overview of the current state of the art of machine learning techniques facilitating these real-world requirements. In particular, we focus on resource-efficient inference based on deep neural networks (DNNs), the predominant machine learning models of the past decade. We give a comprehensive overview of the vast literature that can be mainly split into three non-mutually exclusive categories: (i) quantized neural networks, (ii) network pruning, and (iii) structural efficiency. These techniques can be applied during training or as post-processing, and they are widely used to reduce the computational demands in terms of memory footprint, inference speed, and energy efficiency. We also briefly discuss different concepts of embedded hardware for DNNs and their compatibility with machine learning techniques as well as potential for energy and latency reduction. We substantiate our discussion with experiments on well-known benchmark data sets using compression techniques (quantization, pruning) for a set of resource-constrained embedded systems, such as CPUs, GPUs and FPGAs. The obtained results highlight the difficulty of finding good trade-offs between resource efficiency and prediction quality.

We consider the principled incorporation of prior knowledge in deep learning based Bayesian approaches to causal structure learning via the prior belief. In particular, we investigate how to include knowledge about individual edges and causal dependencies in the prior over the underlying directed acyclic graph (DAG). While conceptually simple, substantial challenges arise because the acyclicity of a DAG limits the modeling choices of the marginal distributions over its edges. Specifying the marginals iteratively unveils their dependencies and ensures a sound formulation of the probability distribution over DAGs. We provide recipes for formulating valid priors over DAGs for two recent deep learning based Bayesian approaches to causal structure learning and demonstrate empirically that using this prior knowledge can enable significantly more sample-efficient causal structure search.

We study sequential decision-making with known rewards and unknown constraints, motivated by situations where the constraints represent expensive-to-evaluate human preferences, such as safe and comfortable driving behavior. We formalize the challenge of interactively learning about these constraints as a novel linear bandit problem which we call constrained linear best-arm identification. To solve this problem, we propose the Adaptive Constraint Learning (ACOL) algorithm. We provide an instance-dependent lower bound for constrained linear best-arm identification and show that ACOL’s sample complexity matches the lower bound in the worst-case. In the average case, ACOL’s sample complexity bound is still significantly tighter than bounds of simpler approaches. In synthetic experiments, ACOL performs on par with an oracle solution and outperforms a range of baselines. As an application, we consider learning constraints to represent human preferences in a driving simulation. ACOL is significantly more sample efficient than alternatives for this application. Further, we find that learning preferences as constraints is more robust to changes in the driving scenario than encoding the preferences directly in the reward function.

Abstraction plays an important role in the generalisation of knowledge and skills and is key to sample efficient learning. In this work, we study joint temporal and state abstraction in reinforcement learning, where temporally-extended actions in the form of options induce temporal abstractions, while aggregation of similar states with respect to abstract options induces state abstractions. Many existing abstraction schemes ignore the interplay of state and temporal abstraction. Consequently, the considered option policies often cannot be directly transferred to new environments due to changes in the state space and transition dynamics. To address this issue, we propose a novel abstraction scheme building on successor features. This includes an algorithm for transferring abstract options across different environments and a state abstraction mechanism that allows us to perform efficient planning with the transferred options.

Online education platforms enable teachers to share a large number of educational resources such as questions to form exercises and quizzes for students. With large volumes of available questions, it is important to have an automated way to quantify their properties and intelligently select them for students, enabling effective and personalized learning experiences. In this work, we propose a framework for mining insights from educational questions at scale. We utilize the state-of-the-art Bayesian deep learning method, in particular partial variational auto-encoders (p-VAE), to analyze real students' answers to a large collection of questions. Based on p-VAE, we propose two novel metrics that quantify question quality and difficulty, respectively, and a personalized strategy to adaptively select questions for students. We apply our proposed framework to a real-world dataset with tens of thousands of questions and tens of millions of answers from an online education platform. Our framework not only demonstrates promising results in terms of statistical metrics but also obtains highly consistent results with domain experts' evaluation.

Many challenging partially observable reinforcement learning problems have sparse rewards and most existing model-free algorithms struggle with such reward sparsity. In this paper, we propose a novel reward shaping approach to infer the intrinsic rewards for the agent from a sequential generative model. Specifically, the sequential generative model processes a sequence of partial observations and actions from the agent's historical transitions to compile a belief state for performing forward dynamics prediction. Then we utilize the error of the dynamics prediction task to infer the intrinsic rewards for the agent. Our proposed method is able to derive intrinsic rewards that could better reflect the agent's surprise or curiosity over its ground-truth state by taking a sequential inference procedure. Furthermore, we formulate the inference procedure for dynamics prediction as a multi-step forward prediction task, where the time abstraction that has been incorporated could effectively help to increase the expressiveness of the intrinsic reward signals. To evaluate our method, we conduct extensive experiments on challenging 3D navigation tasks in ViZDoom and DeepMind Lab. Empirical evaluation results show that our proposed exploration method could lead to significantly faster convergence than various state-of-the-art exploration approaches in the testified navigation domains.

AI technologies are often used to aid people in performing discrete tasks with well-defined goals (e.g., recognising faces in images). Emerging technologies that provide continuous, real-time information enable more open-ended AI experiences. In partnership with a blind child, we explore the challenges and opportunities of designing human-AI interaction for a system intended to support social sensemaking. Adopting a research-through-design perspective, we reflect upon working with the uncertain capabilities of AI systems in the design of this experience. We contribute: (i) a concrete example of an open-ended AI system that enabled a blind child to extend his own capabilities; (ii) an illustration of the delta between imagined and actual use, highlighting how capabilities derive from the human-AI interaction and not the AI system alone; and (iii) a discussion of design choices to craft an ongoing human-AI interaction that addresses the challenge of uncertain outputs of AI systems.

Deep clustering techniques combine representation learning with clustering objectives to improve their performance. Among existing deep clustering techniques, autoencoder-based methods are the most prevalent ones. While they achieve promising clustering results, they suffer from an inherent conflict between preserving details, as expressed by the reconstruction loss, and finding similar groups by ignoring details, as expressed by the clustering loss. This conflict leads to brittle training procedures, dependence on trade-off hyperparameters and less interpretable results. We propose our framework, ACe/DeC, that is compatible with Autoencoder Centroid based Deep Clustering methods and automatically learns a latent representation consisting of two separate spaces. The clustering space captures all cluster-specific information and the shared space explains general variation in the data. This separation resolves the above mentioned conflict and allows our method to learn both detailed reconstructions and cluster specific abstractions. We evaluate our framework with extensive experiments to show several benefits: (1) cluster performance – on various data sets we outperform relevant baselines; (2) no hyperparameter tuning – this improved performance is achieved without introducing new clustering specific hyperparameters; (3) interpretability – isolating the cluster specific information in a separate space is advantageous for data exploration and interpreting the clustering results; and (4) dimensionality of the embedded space – we automatically learn a low dimensional space for clustering. Our ACe/DeC framework isolates cluster information, increases stability and interpretability, while improving cluster performance.

For many reinforcement learning (RL) applications, specifying a reward is difficult. In this paper, we consider an RL setting where the agent can obtain information about the reward only by querying an expert that can, for example, evaluate individual states or provide binary preferences over trajectories. From such expensive feedback, we aim to learn a model of the reward function that allows standard RL algorithms to achieve high expected return with as few expert queries as possible. For this purpose, we propose Information Directed Reward Learning (IDRL), which uses a Bayesian model of the reward function and selects queries that maximize the information gain about the difference in return between potentially optimal policies. In contrast to prior active reward learning methods designed for specific types of queries, IDRL naturally accommodates different query types. Moreover, by shifting the focus from reducing the reward approximation error to improving the policy induced by the reward model, it achieves similar or better performance with significantly fewer queries. We support our findings with extensive evaluations in multiple environments and with different types of queries.

Deep generative models often perform poorly in real-world applications due to the heterogeneity of natural data sets. Heterogeneity arises from data containing different types of features (categorical, ordinal, continuous, etc.) and features of the same type having different marginal distributions. We propose an extension of variational autoencoders (VAEs) called VAEM to handle such heterogeneous data. VAEM is a deep generative model that is trained in a two stage manner, such that the first stage provides a more uniform representation of the data to the second stage, thereby sidestepping the problems caused by heterogeneous data. We provide extensions of VAEM to handle partially observed data, and demonstrate its performance in data generation, missing data prediction and sequential feature selection tasks. Our results show that VAEM broadens the range of real-world applications where deep generative models can be successfully deployed.

Many real-life decision making situations allow further relevant information to be acquired at a specific cost, for example, in assessing the health status of a patient we may decide to take additional measurements such as diagnostic tests or imaging scans before making a final assessment. Acquiring more relevant information enables better decision making, but may be costly. How can we trade off the desire to make good decisions by acquiring further information with the cost of performing that acquisition? To this end, we propose a principled framework, named EDDI (Efficient Dynamic Discovery of high-value Information), based on the theory of Bayesian experimental design. In EDDI, we propose a novel partial variational autoencoder (Partial VAE) to predict missing data entries problematically given any subset of the observed ones, and combine it with an acquisition function that maximizes expected information gain on a set of target variables. We show cost reduction at the same decision quality and improved decision quality at the same cost in multiple machine learning benchmarks and two real-world health-care applications.

In this paper, we address the ice-start problem, i.e., the challenge of deploying machine learning models when only a little or no training data is initially available, and acquiring each feature element of data is associated with costs. This setting is representative of the real-world machine learning applications. For instance, in the health care domain, obtaining every single measurement comes with a cost. We propose Icebreaker, a principled framework for elementwise training data acquisition. Icebreaker introduces a full Bayesian Deep Latent Gaussian Model (BELGAM) with a novel inference method, which combines recent advances in amortized inference and stochastic gradient MCMC to enable fast and accurate posterior inference. By utilizing BELGAM’s ability to fully quantify model uncertainty, we also propose two information acquisition functions for imputation and active prediction problems. We demonstrate that BELGAM performs significantly better than previous variational autoencoder (VAE) based models, when the data set size is small, using both machine learning benchmarks and real world recommender systems and health-care applications. Moreover, Icebreaker not only demonstrates improved performance compared to baselines, but it is also capable of achieving better test performance with less training data available.

The ability for policies to generalize to new environments is key to the broad application of RL agents. A promising approach to prevent an agent’s policy from overfitting to a limited set of training environments is to apply regularization techniques originally developed for supervised learning. However, there are stark differences between supervised learning and RL. We discuss those differences and propose modifications to existing regularization techniques in order to better adapt them to RL. In particular, we focus on regularization techniques relying on the injection of noise into the learned function, a family that includes some of the most widely used approaches such as Dropout and Batch Normalization. To adapt them to RL, we propose Selective Noise Injection (SNI), which maintains the regularizing effect the injected noise has, while mitigating the adverse effects it has on the gradient quality. Furthermore, we demonstrate that the Information Bottleneck (IB) is a particularly well suited regularization technique for RL as it is effective in the low-data regime encountered early on in training RL agents. Combining the IB with SNI, we significantly outperform current state of the art results, including on the recently proposed generalization benchmark Coinrun.

Posterior sampling for reinforcement learning (PSRL) is an effective method for balancing exploration and exploitation in reinforcement learning. Randomised value functions (RVF) can be viewed as a promising approach to scaling PSRL. However, we show that most contemporary algorithms combining RVF with neural network function approximation do not possess the properties which make PSRL effective, and provably fail in sparse reward problems. Moreover, we find that propagation of uncertainty, a property of PSRL previously thought important for exploration, does not preclude this failure. We use these insights to design Successor Uncertainties (SU), a cheap and easy to implement RVF algorithm that retains key properties of PSRL. SU is highly effective on hard tabular exploration benchmarks. Furthermore, on the Atari 2600 domain, it surpasses human performance on 38 of 49 games tested (achieving a median human normalised score of 2.09), and outperforms its closest RVF competitor, Bootstrapped DQN, on 36 of those.

Inverse reinforcement learning (IRL) enables an agent to learn complex behavior by observing demonstrations from a (near-)optimal policy. The typical assumption is that the learner's goal is to match the teacher’s demonstrated behavior. In this paper, we consider the setting where the learner has its own preferences that it additionally takes into consideration. These preferences can for example capture behavioral biases, mismatched worldviews, or physical constraints. We study two teaching approaches: learner-agnostic teaching, where the teacher provides demonstrations from an optimal policy ignoring the learner's preferences, and learner-aware teaching, where the teacher accounts for the learner’s preferences. We design learner-aware teaching algorithms and show that significant performance improvements can be achieved over learner-agnostic teaching.

We study platforms in the sharing economy and discuss the need for incentivizing users to explore options that otherwise would not be chosen. For instance, rental platforms such as Airbnb typically rely on customer reviews to provide users with relevant information about different options. Yet, often a large fraction of options does not have any reviews available. Such options are frequently neglected as viable choices, and in turn are unlikely to be evaluated, creating a vicious cycle. Platforms can engage users to deviate from their preferred choice by offering monetary incentives for choosing a different option instead. To efficiently learn the optimal incentives to offer, we consider structural information in user preferences and introduce a novel algorithm---Coordinated Online Learning (CoOL)---for learning with structural information modeled as convex constraints. We provide formal guarantees on the performance of our algorithm and test the viability of our approach in a user study with data of apartments on Airbnb. Our findings suggest that our approach is well-suited to learn appropriate incentives and increase exploration on the investigated platform.

We consider learning of submodular functions from data. These functions are important in machine learning and have a wide range of applications, e.g. data summarization, feature selection and active learning. Despite their combinatorial nature, submodular functions can be maximized approximately with strong theoretical guarantees in polynomial time. Typically, learning the submodular function and optimization of that function are treated separately, i.e. the function is first learned using a proxy objective and subsequently maximized. In contrast, we show how to perform learning and optimization jointly. By interpreting the output of greedy maximization algorithms as distributions over sequences of items and smoothening these distributions, we obtain a differentiable objective. In this way, we can differentiate through the maximization algorithms and optimize the model to work well with the optimization algorithm. We theoretically characterize the error made by our approach, yielding insights into the tradeoff of smoothness and accuracy. We demonstrate the effectiveness of our approach for jointly learning and optimizing on synthetic maxcut data, and on real world applications such as product recommendation and image collection summarization.

Learning near-optimal behaviour from an expert's demonstrations typically relies on the assumption that the learner knows the features that the true reward function depends on. In this paper, we study the problem of learning from demonstrations in the setting where this is not the case, i.e., where there is a mismatch between the worldviews of the learner and the expert. We introduce a natural quantity, the teaching risk, which measures the potential suboptimality of policies that look optimal to the learner in this setting. We show that bounds on the teaching risk guarantee that the learner is able to find a near-optimal policy using standard algorithms based on inverse reinforcement learning. Based on these findings, we suggest a teaching scheme in which the expert can decrease the teaching risk by updating the learner's worldview, and thus ultimately enable her to find a near-optimal policy.

Motivated by many real world applications such as recommendations in online shopping or entertainment, we consider the problem of selecting sequences of items. In this paper we introduce a novel class of utility functions over sequences of items, strictly generalizing the commonly used class of submodular set functions. We encode the sequential dependencies between items by a directed graph underlying the utility function. Classical algorithms fail to achieve any constant factor approximation guarantees on the problem of selecting sequences of bounded length with maximum utility. We propose an efficient algorithm for this problem that comes with strong theoretical guarantees characterized by the structural properties of the underlying graph. We demonstrate the effectiveness of our algorithm in synthetic and real world experiments on a movie recommendation dataset.

We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for maximizing submodular functions, there are few guarantees for non-submodular ones. However, Greedy enjoys strong empirical performance for many important non-submodular functions, e.g., the Bayesian A-optimality objective in experimental design. We prove theoretical guarantees supporting the empirical performance. Our guarantees are characterized by a combination of the (generalized) curvature $\alpha$ and the submodularity ratio $\gamma$. In particular, we prove that Greedy enjoys a tight approximation guarantee of $\frac{1}{\alpha}(1- e^{-\gamma\alpha})$ for cardinality constrained maximization. In addition, we bound the submodularity ratio and curvature for several important real-world objectives, including the Bayesian A-optimality objective, the determinantal function of a square submatrix and certain linear programs with combinatorial constraints. We experimentally validate our theoretical findings for both synthetic and real-world applications.

We introduce a simple and efficient frame and segment levelRNN model (FS-RNN) for phone classification. It processesthe input atframe levelandsegment levelby bidirectional gatedRNNs. This type of processing is important to exploit the(temporal) information more effectively compared to(i)mod-els which solely process the input at frame level and(ii)mod-els which process the input on segment level using features ob-tained by heuristic aggregation of frame level features. Further-more, we incorporated the activations of the last hidden layerof the FS-RNN as an additional feature type in a neural higher-order CRF (NHO-CRF). In experiments, we demonstrated ex-cellent performance on the TIMIT phone classification task, re-porting a performance of13.8%phone error rate for the FS-RNN model and11.9%when combined with the NHO-CRF. Inboth cases we significantly exceeded the state-of-the-art perfor-mance.

We address the problem of maximizing an unknown submodular function that can only be accessed via noisy evaluations. Our work is motivated by the task of summarizing content, e.g., image collections, by leveraging users' feedback in form of clicks or ratings. For summarization tasks with the goal of maximizing coverage and diversity, submodular set functions are a natural choice. When the underlying submodular function is unknown, users' feedback can provide noisy evaluations of the function that we seek to maximize. We provide a generic algorithm — ExpGreedy — for maximizing an unknown submodular function under cardinality constraints. This algorithm makes use of a novel exploration module— TopX — that proposes good elements based on adaptively sampling noisy function evaluations. TopX is able to accommodate different kinds of observation models such as value queries and pairwise comparisons. We provide PAC-style guarantees on the quality and sampling cost of the solution obtained by ExpGreedy. We demonstrate the effectiveness of our approach in an interactive, crowdsourced image collection summarization application.

Modeling diversity of sets of items is important in many applications such as product recommendation and data summarization. Probabilistic submodular models, a family of models including the determinantal point process, form a natural class of distributions, encouraging effects such as diversity, repulsion and coverage. Current models, however, are limited to small and medium number of items due to the high time complexity for learning and inference. In this paper, we propose FLID, a novel log-submodular diversity model that scales to large numbers of items and can be efficiently learned using noise contrastive estimation. We show that our model achieves state of the art performance in terms of model fit, but can be also learned orders of magnitude faster. We demonstrate the wide applicability of our model using several experiments.

Motivated by an application of eliciting users’ preferences, we investigate the problem of learning hemimetrics, i.e., pairwise distances among a set of n items that satisfy triangle inequalities and non-negativity constraints. In our application, the (asymmetric) distances quantify private costs a user incurs when substituting one item by another. We aim to learn these distances (costs) by asking the users whether they are willing to switch from one item to another for a given incentive offer. Without exploiting structural constraints of the hemimetric polytope, learning the distances between each pair of items requires Θ(n^2) queries. We propose an active learning algorithm that substantially reduces this sample complexity by exploiting the structural constraints on the version space of hemimetrics. Our proposed algorithm achieves provably-optimal sample complexity for various instances of the task. For example, when the items are embedded into K tight clusters, the sample complexity of our algorithm reduces to O(n K). Extensive experiments on a restaurant recommendation data set support the conclusions of our theoretical analysis.

We explore virtual adversarial training (VAT) applied to neu-ral higher-order conditional random fields for sequence label-ing. VAT is a recently introduced regularization method pro-moting local distributional smoothness: It counteracts the prob-lem that predictions of many state-of-the-art classifiers are un-stable to adversarial perturbations. Unlike random noise, ad-versarial perturbations are minimal and bounded perturbationsthat flip the predicted label. We utilize VAT to regularize neuralhigher-order factors in conditional random fields. These fac-tors are for example important for phone classification wherephone representations strongly depend on the context phones.However, without using VAT for regularization, the use of suchfactors was limited as they were prone to overfitting. In exten-sive experiments, we successfully apply VAT to improve per-formance on the TIMIT phone classification task. In particular,we achieve a phone error rate of13.0%, exceeding the state-of-the-art performance by a wide margin.Index Terms: Virtual adversarial training, local distributionalsmoothing, deep higher-order factors, neural higher-order con-ditional random field, phone classificatio.

We study a rich family of distributions that capture variable interactions significantly more expressive than those representable with low-treewidth or pairwise graphical models, or log-supermodular models. We call these cooperative graphical models. Yet, this family retains structure, which we carefully exploit for efficient inference techniques. Our algorithms combine the polyhedral structure of submodular functions in new ways with variational inference methods to obtain both lower and upper bounds on the partition function. While our fully convex upper bound is minimized as an SDP or via tree-reweighted belief propagation, our lower bound is tightened via belief propagation or mean-field algorithms. The resulting algorithms are easy to implement and, as our experiments show, effectively obtain good bounds and marginals for synthetic and real-world examples.

We consider the problem of variational inference in probabilistic models with both log-submodular and log-supermodular higher-order potentials. These models can represent arbitrary distributions over binary variables, and thus generalize the commonly used pairwise Markov random fields and models with log-supermodular potentials only, for which efficient approximate inference algorithms are known. While inference in the considered models is #P-hard in general, we present efficient approximate algorithms exploiting recent advances in the field of discrete optimization. We demonstrate the effectiveness of our approach in a large set of experiments, where our model allows reasoning about preferences over sets of items with complements and substitutes.

Sum-product networks (SPNs) are a promising avenue for probabilistic modeling and have been successfully applied to various tasks. However, some theoretic properties about SPNs are not yet well understood. In this paper we fill some gaps in the theoretic foundation of SPNs. First, we show that the weights of any complete and consistent SPN can be transformed into locally normalized weights without changing the SPN distribution. Second, we show that consistent SPNs cannot model distributions significantly (exponentially) more compactly than decomposable SPNs. As a third contribution, we extend the inference mechanisms known for SPNs with finite states to generalized SPNs with arbitrary input distributions.

We explore neural higher-order input-dependent factors inlinear-chain conditional random fields (LC-CRFs) for sequencelabeling. It is a fusion of two powerful models as higher-orderLC-CRFs with linear factors are well-established for sequencelabeling tasks, but they lack to model non-linear dependencies.Therefore, we present neural higher-order input-dependent fac-tors which map sub-sequences of inputs to sub-sequences ofoutputs using distinct multilayer perceptron sub-networks. Thisis important in many tasks, in particular, for phoneme classifi-cation where the phone representation strongly depends on thecontext phonemes. Experimental results for phoneme classifi-cation with LC-CRFs and neural higher-order factors confirmthis fact and we achieve the best ever reported phoneme clas-sification performance on TIMIT, i.e. a phoneme error rate of15:8%. Furthermore, we show that the success is not obviousas linear high-order factors degrade phoneme classification per-formance on TIMIT.

Bayesian network classifier (BNCs) are typically implemented on nowadays desktop computers. However, many real world applications require classifier implementation on embedded or low power systems. Aspects for this purpose have not been studied rigorously. We partly close this gap by analyzing reduced precision implementations of BNCs. In detail, we investigate the quantization of the parameters of BNCs with discrete valued nodes including the implications on the classification rate (CR). We derive worst-case and probabilistic bounds on the CR for different bit-widths. These bounds are evaluated on several benchmark datasets. Furthermore, we compare the classification performance and the robustness of BNCs with generatively and discriminatively optimized parameters, i.e. parameters optimized for high data likelihood and parameters optimized for classification, with respect to parameter quantization. Generatively optimized parameters are more robust for very low bit-widths, i.e. less classifications change because of quantization. However, classification performance is better for discriminatively optimized parameters for all but very low bit-widths. Additionally, we perform analysis for margin-optimized tree augmented network (TAN) structures which outperform generatively optimized TAN structures in terms of CR and robustness.

Maximum margin Bayesian networks (MMBNs) are Bayesian networks with discriminatively optimized parameters. They have shown good classification performance in various applications. However, there has not been any theoretic analysis of their asymptotic performance, e.g. their Bayes consistency. For specific classes of MMBNs, i.e. MMBNs with fully connected graphs and discrete-valued nodes, we show Bayes consistency for binary-class problems and a sufficient condition for Bayes consistency in the multi-class case. We provide simple examples showing that MMBNs in their current formulation are not Bayes consistent in general. These examples are especially interesting, as the model used for the MMBNs can represent the assumed true distributions. This indicates that the current formulations of MMBNs may be deficient. Furthermore, experimental results on the generalization performance are presented.

Bayesian network classifiers are probabilistic classifiers achieving good classification rates in various applications. These classifiers consist of a directed acyclic graph and a set of conditional probability densities, which in case of discrete-valued nodes can be represented by conditional probability tables. In this paper, we investigate the effect of quantizing these conditional probabilities. We derive worst-case and best-case bounds on the classification rate using interval arithmetic. Furthermore, we determine performance bounds that hold with a user specified confidence using quantization theory. Our results emphasize that only small bit-widths are necessary to achieve good classification rates.

Although discriminative learning in graphical models generally improves classification results, the generative semantics of the model are compromised. In this paper, we introduce a novel approach of hybrid generative-discriminative learning for Bayesian networks. We use an SVM-type large margin formulation for discriminative training, introducing a likelihood-weighted \ell^1-norm for the SVM-norm-penalization. This simultaneously optimizes the data likelihood and therefore partly maintains the generative character of the model. For many network structures, our method can be formulated as a convex problem, guaranteeing a globally optimal solution. In terms of classification, the resulting models outperform state-of-the art generative and discriminative learning methods for Bayesian networks, and are comparable with linear and kernelized SVMs. Furthermore, the models achieve likelihoods close to the maximum likelihood solution and show robust behavior in classification experiments with missing features.

We present a maximum margin parameter learning algorithm for Bayesian network classifiers using a conjugate gradient (CG) method for optimization. In contrast to previous approaches, we maintain the normalization constraints on the parameters of the Bayesian network during optimization, i.e., the probabilistic interpretation of the model is not lost. This enables us to handle missing features in discriminatively optimized Bayesian networks. In experiments, we compare the classification performance of maximum margin parameter learning to conditional likelihood and maximum likelihood learning approaches. Discriminative parameter learning significantly outperforms generative maximum likelihood estimation for naive Bayes and tree augmented naive Bayes structures on all considered data sets. Furthermore, maximizing the margin dominates the conditional likelihood approach in terms of classification performance in most cases. We provide results for a recently proposed maximum margin optimization approach based on convex relaxation. While the classification results are highly similar, our CG-based optimization is computationally up to orders of magnitude faster. Margin-optimized Bayesian network classifiers achieve classification performance comparable to support vector machines (SVMs) using fewer parameters. Moreover, we show that unanticipated missing feature values during classification can be easily processed by discriminatively optimized Bayesian network classifiers, a case where discriminative classifiers usually require mechanisms to complete unknown feature values in the data first.