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Entropy estimation is an important problem in information theory and statistical science. Many popular entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for high dimensional problems. In this work we propose a transformbased method for high dimensional entropy estimation, which consists of the following two main ingredients. First by modifying the k-NN based entropy estimator, we propose a new estimator which enjoys small estimation bias for samples that are close to a uniform distribution. Second we design a normalizing flow based mapping that pushes samples toward a uniform distribution, and the relation between the entropy of the original samples and the transformed ones is also derived. As a result the entropy of a given set of samples is estimated by first transforming them toward a uniform distribution and then applying the proposed estimator to the transformed samples. Numerical experiments demonstrate the effectiveness of the method for high dimensional entropy estimation problems.

Automated high-stake decision-making, such as medical diagnosis, requires models with high interpretability and reliability. We consider the sparse high-order interaction model as an interpretable and reliable model with a good prediction ability. However, finding statistically significant high-order interactions is challenging because of the intrinsically high dimensionality of the combinatorial effects. Another problem in data-driven modeling is the effect of ``cherry-picking" (i.e., selection bias). Our main contribution is extending the recently developed parametric programming approach for selective inference to high-order interaction models. An exhaustive search over the cherry tree (all possible interactions) can be daunting and impractical, even for small-sized problems. We introduced an efficient pruning strategy and demonstrated the computational efficiency and statistical power of the proposed method using both synthetic and real data.

In this paper, we generalize the recently studied stochastic matching problem to more accurately model a significant medical process, kidney exchange, and several other applications. Up until now the stochastic matching problem that has been studied was as follows: given a graph G= (V,E), each edge is included in the realized sub-graph of G independently with probability pe, and the goal is to find a degree-bounded sub-graph Q of G that has an expected maximum matching that approximates the expected maximum matching of G. This model does not account for possibilities of vertex dropouts, which can be found in several applications, e.g. in kidney exchange when donors or patients opt out of the exchange process as well as in online freelancing and online dating when online profiles are found to be faked. Thus, we will study a more generalized model of stochastic matching in which vertices and edges are both realized independently with some probabilities pv, pe, respectively, which more accurately fits important applications than the previously studied model. We will discuss the first algorithms and analysis for this generalization of the stochastic matching model and prove that they achieve good approximation ratios. In particular, we show that the approximation factor of a natural algorithm for this problem is at least 0.6568 in unweighted graphs, and 1/2+ε in weighted graphs for some constant ε >0. We further improve our result for unweighted graphs to 2/3 using edge degree constrained sub-graphs (EDCS).

Bandit algorithms are widely used in sequential decision problems to maximize the cumulative reward. One potential application is mobile health, where the goal is to promote the user's health through personalized interventions based on user specific information acquired through wearable devices. Important considerations include the type of, and frequency with which data is collected (e.g. GPS, or continuous monitoring), as such factors can severely impact app performance and users’ adherence. In order to balance the need to collect data that is useful with the constraint of impacting app performance, one needs to be able to assess the usefulness of variables. Bandit feedback data are sequentially correlated, so traditional testing procedures developed for independent data cannot apply. Recently, a statistical testing procedure was developed for the actor-critic bandit algorithm. An actor-critic algorithm maintains two separate models, one for the actor, the action selection policy, and the other for the critic, the reward model. The performance of the algorithm as well as the validity of the test are guaranteed only when the critic model is correctly specified. However, misspecification is frequent in practice due to incorrect functional form or missing covariates. In this work, we propose a modified actor-critic algorithm which is robust to critic misspecification and derive a novel testing procedure for the actor parameters in this case.

In this paper, we propose two new definitions of local differential privacy for belief functions. One is based on Shafer’s semantics of randomly coded messages and the other from the perspective of imprecise probabilities. We show that such basic properties as composition and post-processing also hold for our new definitions. Moreover, we provide a hypothesis testing framework for these definitions and study the effect of "don’t know" in the trade-off between privacy and utility in discrete distribution estimation.

Influence diagrams have recently been used to analyse the safety and fairness properties of AI systems. A key building block for this analysis is a graphical criterion for value of information (VoI). This paper establishes the first complete graphical criterion for VoI in influence diagrams with multiple decisions. Along the way, we establish two techniques for proving properties of multi-decision influence diagrams: ID homomorphisms are structure-preserving transformations of influence diagrams, while a Tree of Systems is a collection of paths that captures how information and control can flow in an influence diagram.

Uncertainty estimation is an essential step in the evaluation of the robustness for deep learning models in computer vision, especially when applied in risk-sensitive areas. However, most state-of-the-art deep learning models either fail to obtain uncertainty estimation or need significant modification (e.g., formulating a proper Bayesian treatment) to obtain it. Most previous methods are not able to take an arbitrary model off the shelf and generate uncertainty estimation without retraining or redesigning it. To address this gap, we perform a systematic exploration into training-free uncertainty estimation for dense regression, an unrecognized yet important problem, and provide a theoretical construction justifying such estimations. We propose three simple and scalable methods to analyze the variance of outputs from a trained network under tolerable perturbations: infer-transformation, infer-noise, and infer-dropout. They operate solely during the inference, without the need to re-train, re-design, or fine-tune the models, as typically required by state-of-the-art uncertainty estimation methods. Surprisingly, even without involving such perturbations in training, our methods produce comparable or even better uncertainty estimation when compared to training-required state-of-the-art methods. Code is available at https://github.com/lumi9587/train-free-uncertainty.

Modern neural networks can assign high confidence to inputs drawn from outside the training distribution, posing threats to models in real-world deployments. While much research attention has been placed on designing new out-of-distribution (OOD) detection methods, the precise definition of OOD is often left in vagueness and falls short of the desired notion of OOD in reality. In this paper, we present a new formalization and model the data shifts by taking into account both the invariant and environmental (spurious) features. Under such formalization, we systematically investigate how spurious correlation in the training set impacts OOD detection. Our results suggest that the detection performance is severely worsened when the correlation between spurious features and labels is increased in the training set. We further show insights on detection methods that are more effective in reducing the impact of spurious correlation, and provide theoretical analysis on why reliance on environmental features leads to high OOD detection error. Our work aims to facilitate better understanding of OOD samples and their formalization, as well as the exploration of methods that enhance OOD detection. Code is available at https://github.com/deeplearning-wisc/Spurious_OOD.

An issue that has so far received only limited attention in probabilistic logic programming (PLP) is the modelling of so-called epistemic uncertainty, the uncertainty about the model itself. Accurately quantifying this model uncertainty is paramount to robust inference, learning and ultimately decision making. We introduce BetaProbLog, a PLP language that can model epistemic uncertainty. BetaProbLog has sound semantics, an effective inference algorithm that combines Monte Carlo techniques with knowledge compilation, and a parameter learning algorithm. We empirically outperform state-of-the-art methods on probabilistic inference tasks in second-order Bayesian networks, digit classification and discriminative learning in the presence of epistemic uncertainty.

Given a first-order sentence ? and a domain size n, how can one sample a model of ? on the domain {1, . . . , n} efficiently as n scales? We consider two variants of this problem: the uniform sampling regime, in which the goal is to sample a model uniformly at random, and the symmetric weighted sampling regime, in which models are weighted according to the number of groundings of each predicate appearing in them. Solutions to this problem have applications to the scalable generation of combinatorial structures, as well as sampling in several statistical-relational models such as Markov logic networks and probabilistic logic programs. In this paper, we identify certain classes of sentences that are domain-liftable under sampling, in the sense that they admit a sampling algorithm that runs in time polynomial in n. In particular, we prove that every sentence of the form ∀x∀y: ?(x, y) for some quantifier-free formula ?(x,y) is domain-liftable under sampling. We then further show that this result continues to hold in the presence of one or more cardinality constraints as well as a single tree axiom constraint.

We study identifiability of linear Andersson-Madigan-Perlman (AMP) chain graph models, which are a common generalization of linear structural equation models and Gaussian graphical models. AMP models are described by DAGs on chain components which themselves are undirected graphs. For a known chain component decomposition, we show that the DAG on the chain components is identifiable if the determinants of the residual covariance matrices of the chain components are equal (or more generally, monotone non-decreasing in topological order). This condition extends the equal variance identifiability criterion for Bayes nets, and it can be generalized from determinants to any super-additive function on positive semidefinite matrices. When the component decomposition is unknown, we describe conditions that allow recovery of the full structure using a polynomial time algorithm based on submodular function minimization. We also conduct experiments comparing our algorithm's performance against existing baselines.

Recent advances in neural-symbolic learning, such as DeepProbLog, extend probabilistic logic programs with neural predicates. Like graphical models, these probabilistic logic programs define a probability distribution over possible worlds, for which inference is computationally hard. We propose DeepStochLog, an alternative neural-symbolic framework based on stochastic definite clause grammars, a kind of stochastic logic program. More specifically, we introduce neural grammar rules into stochastic definite clause grammars to create a framework that can be trained end-to-end. We show that inference and learning in neural stochastic logic programming scale much better than for neural probabilistic logic programs. Furthermore, the experimental evaluation shows that DeepStochLog achieves state-of-the-art results on challenging neural-symbolic learning tasks.

Off-policy learning plays a pivotal role in optimizing and evaluating policies prior to the online deployment. However, during the real-time serving, we observe varieties of interventions and constraints that cause inconsistency between the online and offline setting, which we summarize and term as runtime uncertainty. Such uncertainty cannot be learned from the logged data due to its abnormality and rareness nature. To assert a certain level of robustness, we perturb the off-policy estimators along an adversarial direction in view of the runtime uncertainty. It allows the resulting estimators to be robust not only to observed but also unexpected runtime uncertainties. Leveraging this idea, we bring runtime-uncertainty robustness to three major off-policy learning methods: the inverse propensity score method, reward-model method, and doubly robust method. We theoretically justify the robustness of our methods to runtime uncertainty, and demonstrate their effectiveness using both the simulation and the real-world online experiments.

Bayesian neural networks (BNNs) have drawn extensive interest due to the unique probabilistic representation framework. However, Bayesian neural networks have limited publicized deployments because of the relatively poor model performance in real-world applications. In this paper, we argue that the randomness of sampling in Bayesian neural networks causes errors in the updating of model parameters during training and some sampled models with poor performance in testing. To solve this, we propose to train Bayesian neural networks with Adversarial Distribution as a theoretical solution. To avoid the difficulty of calculating Adversarial Distribution analytically, we further present the Adversarial Sampling method as an approximation in practice. We conduct extensive experiments with multiple network structures on different datasets, e.g., CIFAR-10 and CIFAR-100. Experimental results validate the correctness of the theoretical analysis and the effectiveness of the Adversarial Sampling on improving model performance. Additionally, models trained with Adversarial Sampling still keep their ability to model uncertainties and perform better when predictions are retained according to the uncertainties, which further verifies the generality of the Adversarial Sampling approach.