Situations in which people with opposing prior beliefs observe the same evidence and then strengthen those existing beliefs are frequently offered as evidence of human irrationality. This phenomenon, termed belief polarization, is typically assumed to be non-normative. We demonstrate, however, that a variety of cases of belief polarization are consistent with a Bayesian approach to belief revision. Simulation results indicate that belief polarization is not only possible but relatively common within the class of Bayesian models that we consider.

This paper introduces a Monte-Carlo algorithm for online planning in large POMDPs. The algorithm combines a Monte-Carlo update of the agent's belief state with a Monte-Carlo tree search from the current belief state. The new algorithm, POMCP, has two important properties. First, Monte-Carlo sampling is used to break the curse of dimensionality both during belief state updates and during planning. Second, only a black box simulator of the POMDP is required, rather than explicit probability distributions.

Experts (human or computer) are often required to assess the probability of uncertain events. When a collection of experts independently assess events that are structurally interrelated, the resulting assessment may violate fundamental laws of probability. Such an assessment is termed incoherent. In this work we investigate how the problem of incoherence may be affected by allowing experts to specify likelihood models and then update their assessments based on the realization of a globally-observable random sequence.

While loopy Belief Propagation (LBP) has been utilized in a wide variety of applications with empirical success, it comes with few theoretical guarantees. Especially, if the interactions of random variables in a graphical model are strong, the behaviors of the algorithm can be difficult to analyze due to underlying phase transitions. In this paper, we develop a novel approach to the uniqueness problem of the LBP fixed point; our new "necessary and sufficient" condition is stated in terms of graphs and signs, where the sign denotes the types (attractive/repulsive) of the interaction (i.e., compatibility function) on the edge. In all previous works, uniqueness is guaranteed only in the situations where the strength of the interactions are "sufficiently" small in certain senses. In contrast, our condition covers arbitrary strong interactions on the specified class of signed graphs.

The empirical success of the belief propagation approximate inference algorithm has inspired numerous theoretical and algorithmic advances. Yet, for continuous non-Gaussian domains performing belief propagation remains a challenging task: recent innovations such as nonparametric or kernel belief propagation, while useful, come with a substantial computational cost and offer little theoretical guarantees, even for tree structured models. For tree structured networks, our approach is guaranteed to be exact for this powerful class of non-Gaussian models. Importantly, the method is as efficient as standard Gaussian BP, and its convergence properties do not depend on the complexity of the univariate marginals, even when a nonparametric representation is used.

Discovering hierarchical regularities in data is a key problem in interacting with large datasets, modeling cognition, and encoding knowledge. A previous Bayesian solution---Kingman's coalescent---provides a convenient probabilistic model for data represented as a binary tree. Unfortunately, this is inappropriate for data better described by bushier trees. We generalize an existing belief propagation framework of Kingman's coalescent to the beta coalescent, which models a wider range of tree structures. Because of the complex combinatorial search over possible structures, we develop new sampling schemes using sequential Monte Carlo and Dirichlet process mixture models, which render inference efficient and tractable.

Max-product'belief propagation' (BP) is a popular distributed heuristic for finding the Maximum A Posteriori (MAP) assignment in a joint probability distribution represented by a Graphical Model (GM). It was recently shown that BP converges to the correct MAP assignment for a class of loopy GMs with the following common feature: the Linear Programming (LP) relaxation to the MAP problem is tight (has no integrality gap). Unfortunately, tightness of the LP relaxation does not, in general, guarantee convergence and correctness of the BP algorithm. The failure of BP in such cases motivates reverse engineering a solution – namely, given a tight LP, can we design a'good' BP algorithm. We prove that the algorithm converges to the correct optimum if the respective LP relaxation, which may include inequalities associated with non-intersecting odd-sized cycles, is tight.

In this paper, we address this question in the context of General Lotto games, a class of two-player competitive resource allocation models. We consider an asymmetric information setting where the opponent is uncertain about the resource budget of the other player, and holds a prior belief on its value. We assume the other player, called the signaler, is able to send a noisy signal about its budget to the opponent. With its updated belief, the opponent then must decide to invest in costly resources that it will deploy against the signaler's resource budget in a General Lotto game. We derive the subgame perfect equilibrium to this extensive-form game. In particular, we identify necessary and sufficient conditions for which a signaling policy improves the signaler's resulting performance in comparison to the scenario where it does not send any signal. Moreover, we provide the optimal signaling policy when these conditions are met. Notably we find that for some scenarios, the signaler can effectively double its performance.

We introduce and evaluate an eXplainable Goal Recognition (XGR) model that uses the Weight of Evidence (WoE) framework to explain goal recognition problems. Our model provides human-centered explanations that answer why? and why not? questions. We computationally evaluate the performance of our system over eight different domains. Using a human behavioral study to obtain the ground truth from human annotators, we further show that the XGR model can successfully generate human-like explanations. We then report on a study with 60 participants who observe agents playing Sokoban game and then receive explanations of the goal recognition output. We investigate participants' understanding obtained by explanations through task prediction, explanation satisfaction, and trust.

We present a differentiable approach to learn the probabilistic factors used for inference by a nonparametric belief propagation algorithm. Existing nonparametric belief propagation methods rely on domain-specific features encoded in the probabilistic factors of a graphical model. In this work, we replace each crafted factor with a differentiable neural network enabling the factors to be learned using an efficient optimization routine from labeled data. By combining differentiable neural networks with an efficient belief propagation algorithm, our method learns to maintain a set of marginal posterior samples using end-to-end training. We evaluate our differentiable nonparametric belief propagation (DNBP) method on a set of articulated pose tracking tasks and compare performance with learned baselines. Results from these experiments demonstrate the effectiveness of using learned factors for tracking and suggest the practical advantage over hand-crafted approaches. The project webpage is available at: https://progress.eecs.umich.edu/projects/dnbp/ .