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.

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/ .

Eva is a multimodal conversational system that helps users to accomplish their domain goals through collaborative dialogue. The system does this by inferring users' intentions and plans to achieve those goals, detects whether obstacles are present, finds plans to overcome them or to achieve higher-level goals, and plans its actions, including speech acts,to help users accomplish those goals. In doing so, the system maintains and reasons with its own beliefs, goals and intentions, and explicitly reasons about those of its user. Belief reasoning is accomplished with a modal Horn-clause meta-interpreter. The planning and reasoning subsystems obey the principles of persistent goals and intentions, including the formation and decomposition of intentions to perform complex actions, as well as the conditions under which they can be given up. In virtue of its planning process, the system treats its speech acts just like its other actions -- physical acts affect physical states, digital acts affect digital states, and speech acts affect mental and social states. This general approach enables Eva to plan a variety of speech acts including requests, informs, questions, confirmations, recommendations, offers, acceptances, greetings, and emotive expressions. Each of these has a formally specified semantics which is used during the planning and reasoning processes. Because it can keep track of different users' mental states, it can engage in multi-party dialogues. Importantly, Eva can explain its utterances because it has created a plan standing behind each of them. Finally, Eva employs multimodal input and output, driving an avatar that can perceive and employ facial and head movements along with emotive speech acts.

In this paper, we provide two views of constrained differential private (DP) mechanisms. The first one is as belief revision. A constrained DP mechanism is obtained by standard probabilistic conditioning, and hence can be naturally implemented by Monte Carlo algorithms. The other is as belief update. A constrained DP is defined according to l2-distance minimization postprocessing or projection and hence can be naturally implemented by optimization algorithms. The main advantage of these two perspectives is that we can make full use of the machinery of belief revision and update to show basic properties for constrained differential privacy especially some important new composition properties. Within the framework established in this paper, constrained DP algorithms in the literature can be classified either as belief revision or belief update. At the end of the paper, we demonstrate their differences especially in utility in a couple of scenarios.

Density Ratio Estimation (DRE) is an important machine learning technique with many downstream applications. We consider the challenge of DRE with missing not at random (MNAR) data. In this setting, we show that using standard DRE methods leads to biased results while our proposal (M-KLIEP), an adaptation of the popular DRE procedure KLIEP, restores consistency. Moreover, we provide finite sample estimation error bounds for M-KLIEP, which demonstrate minimax optimality with respect to both sample size and worst-case missingness. We then adapt an important downstream application of DRE, Neyman-Pearson (NP) classification, to this MNAR setting. Our procedure both controls Type I error and achieves high power, with high probability. Finally, we demonstrate promising empirical performance both synthetic data and real-world data with simulated missingness.

Thus, we introduce Multi-robot systems (MRS) have the potential to assist a coordinated epistemic prediction and planning method in many safety-critical applications such as search and rescue, in which a robot propagates a finite set of belief states military intelligence and surveillance, and inspection representing possible states of other agents in the system and operations where it may be hazardous and costly to deploy empathy states representing a finite set of possible states from humans. Looking to the state-of-the-art, we note that most other agents' perspectives. Subsequently, using epistemic MRS research assumes constant communication between planning, we can formulate a consensus strategy such that robots [1]-[3]. However, within the aforementioned application every distributed belief in the system achieves consensus. For space, long-range communication is often unreliable example, consider Figure 1 where two robots are canvassing or unavailable. Humans adequately cope with such problems, an environment. During disconnection, Robot 1 maintains a performing these tasks collaboratively by extrapolating and set of possible (belief) states for Robot 2 and also a set of empathizing with what other actors might believe if the local (empathy) states that Robot 2 might believe about Robot 1. plan must change at run-time. This subconscious process can Once Robot 2 experiences a failure, it tracks another state be modally represented as epistemic planning, computing in its empathy set. We reason that though Robot 1 holds a and reasoning about multiple predictions and actions while false belief about Robot 2's state, there exists an epistemic accounting for a priori beliefs, current observations, and strategy that can allow robot 1 to find robot 2 (i.e., updating other actors' sensing and mobility capabilities.

We consider the problem EnumIP of enumerating prime implicants of Boolean functions represented by decision decomposable negation normal form (dec-DNNF) circuits. We study EnumIP from dec-DNNF within the framework of enumeration complexity and prove that it is in OutputP, the class of output polynomial enumeration problems, and more precisely in IncP, the class of polynomial incremental time enumeration problems. We then focus on two closely related, but seemingly harder, enumeration problems where further restrictions are put on the prime implicants to be generated. In the first problem, one is only interested in prime implicants representing subset-minimal abductive explanations, a notion much investigated in AI for more than three decades. In the second problem, the target is prime implicants representing sufficient reasons, a recent yet important notion in the emerging field of eXplainable AI, since they aim to explain predictions achieved by machine learning classifiers. We provide evidence showing that enumerating specific prime implicants corresponding to subset-minimal abductive explanations or to sufficient reasons is not in OutputP.