Inference is a main task in structured prediction and it is naturally modeled with a graph. In the context of Markov random fields, noisy observations corresponding to nodes and edges are usually involved, and the goal of exact inference is to recover the unknown true label for each node precisely. The focus of this paper is on the fundamental limits of exact recovery irrespective of computational efficiency, assuming the generative process proposed by Globerson et al. (2015). We derive the necessary condition for any algorithm and the sufficient condition for maximum likelihood estimation to achieve exact recovery with high probability, and reveal that the sufficient and necessary conditions are tight up to a logarithmic factor for a wide range of graphs. Finally, we show that there exists a gap between the fundamental limits and the performance of the computationally tractable method of Bello and Honorio (2019), which implies the need for further development of algorithms for exact inference.

Active Inference (ActInf) is an emerging theory that explains perception and action in biological agents, in terms of minimizing a free energy bound on Bayesian surprise. Goal-directed behavior is elicited by introducing prior beliefs on the underlying generative model. In contrast to prior beliefs, which constrain all realizations of a random variable, we propose an alternative approach through chance constraints, which allow for a (typically small) probability of constraint violation, and demonstrate how such constraints can be used as intrinsic drivers for goal-directed behavior in ActInf. We illustrate how chance-constrained ActInf weights all imposed (prior) constraints on the generative model, allowing e.g., for a trade-off between robust control and empirical chance constraint violation. Secondly, we interpret the proposed solution within a message passing framework. Interestingly, the message passing interpretation is not only relevant to the context of ActInf, but also provides a general purpose approach that can account for chance constraints on graphical models. The chance constraint message updates can then be readily combined with other pre-derived message update rules, without the need for custom derivations. The proposed chance-constrained message passing framework thus accelerates the search for workable models in general, and can be used to complement message-passing formulations on generative neural models.

Binary classifiers trained on a certain proportion of positive items introduce a bias when applied to data sets with different proportions of positive items. Most solutions for dealing with this issue assume that some information on the latter distribution is known. However, this is not always the case, certainly when this proportion is the target variable. In this paper a maximum likelihood estimator for the true proportion of positives in data sets is suggested and tested on synthetic and real world data.

Abstract--Shared mental models are critical to team success; however, in practice, team members may have misaligned models due to a variety of factors. In safety-critical domains (e.g., aviation, healthcare), lack of shared mental models can lead to preventable errors and harm. Towards the goal of mitigating such preventable errors, here, we present a Bayesian approach to infer misalignment in team members' mental models during complex healthcare task execution. As an exemplary application, we demonstrate our approach using two simulated team-based scenarios, derived from actual teamwork in cardiac surgery. In these simulated experiments, our approach inferred model misalignment with over 75% recall, thereby providing a building block for enabling computer-assisted interventions to augment human cognition in the operating room and improve teamwork.

We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model parameters by maximising our lower bound retains many of the sparse variational approach benefits while reducing the bias introduced into parameter learning. The basis of our bound is a more careful analysis of the log-determinant term appearing in the log marginal likelihood, as well as using the method of conjugate gradients to derive tight lower bounds on the term involving a quadratic form. Our approach is a step forward in unifying methods relying on lower bound maximisation (e.g. variational methods) and iterative approaches based on conjugate gradients for training Gaussian processes. In experiments, we show improved predictive performance with our model for a comparable amount of training time compared to other conjugate gradient based approaches.

In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision space. We consider cases where the spatial variation of these response distributions does not only concern their mean and/or variance but also other features including for instance shape or uni-modality versus multi-modality. Our contributions build upon a non-parametric Bayesian approach to modelling the thereby induced fields of probability distributions, and in particular to a spatial extension of the logistic Gaussian model. The considered models deliver probabilistic predictions of response distributions at candidate points, allowing for instance to perform (approximate) posterior simulations of probability density functions, to jointly predict multiple moments and other functionals of target distributions, as well as to quantify the impact of collecting new samples on the state of knowledge of the distribution field of interest. In particular, we introduce adaptive sampling strategies leveraging the potential of the considered random distribution field models to guide system evaluations in a goal-oriented way, with a view towards parsimoniously addressing calibration and related problems from non-linear (stochastic) inversion and global optimisation.

Bayesian Neural Networks (BNNs) [37, 47] offer a probabilistic interpretation for deep learning models by imposing a prior distribution on the weight parameters and aim to obtain a posterior distribution instead of only point estimates. By marginalizing over this posterior for prediction, BNNs perform a procedure of ensemble learning. These principles facilitate the model to improve generalization, robustness and allow for uncertainty quantification. However, computing exactly the posterior of non-linear Bayesian networks is infeasible and approximate inference has been devised. The core challenge is how to construct an expressive approximation for the true posterior while maintaining computational efficiency and scalability, especially for modern deep learning architectures. Variational inference is a popular deterministic approximation approach to to deal with this challenge. The first practical methods are proposed in [15, 5, 28], in which, the approximate posterior is assumed to be a fully factorized distribution, also called mean-field variational inference. Generally, the mean-field approximation family encourages some advantages in inference including computational tractability and effective optimization with the stochastic gradient-based methods. However, it will ignore strong statistical dependencies among random weights of the neural networks, which leads to an inability to capture the complicated structure of the true posterior and to estimate true model uncertainty.

Analysis of heterogeneous patterns in complex spatio-temporal data finds usage across various domains in applied science and engineering, including training autonomous vehicles to navigate in complex traffic scenarios. Motivated by applications arising in the transportation domain, in this paper we develop a model for learning heterogeneous and dynamic patterns of velocity field data. We draw from basic nonparameric Bayesian modeling elements such as hierarchical Dirichlet process and infinite hidden Markov model, while the smoothness of each homogeneous velocity field element is captured with a Gaussian process prior. Of particular focus is a scalable approximate inference method for the proposed model; this is achieved by employing sequential MAP estimates from the infinite HMM model and an efficient sequential GP posterior computation technique, which is shown to work effectively on simulated data sets. Finally, we demonstrate the effectiveness of our techniques to the NGSIM dataset of complex multi-vehicle interactions.

People have made remarkable progress in game AIs, especially in domain of perfect information game. However, trick-taking poker game, as a popular form of imperfect information game, has been regarded as a challenge for a long time. Since trick-taking game requires high level of not only reasoning, but also inference to excel, it can be a new milestone for imperfect information game AI. We study Gongzhu, a trick-taking game analogous to, but slightly simpler than contract bridge. Nonetheless, the strategies of Gongzhu are complex enough for both human and computer players. We train a strong Gongzhu AI ScrofaZero from \textit{tabula rasa} by deep reinforcement learning, while few previous efforts on solving trick-taking poker game utilize the representation power of neural networks. Also, we introduce new techniques for imperfect information game including stratified sampling, importance weighting, integral over equivalent class, Bayesian inference, etc. Our AI can achieve human expert level performance. The methodologies in building our program can be easily transferred into a wide range of trick-taking games.

We study the problem of distributed cooperative learning, where a group of agents seek to agree on a set of hypotheses that best describes a sequence of private observations. In the scenario where the set of hypotheses is large, we propose a belief update rule where agents share compressed (either sparse or quantized) beliefs with an arbitrary positive compression rate. Our algorithm leverages a unified and straightforward communication rule that enables agents to access wide-ranging compression operators as black-box modules. We prove the almost sure asymptotic exponential convergence of beliefs around the set of optimal hypotheses. Additionally, we show a non-asymptotic, explicit, and linear concentration rate in probability of the beliefs on the optimal hypothesis set. We provide numerical experiments to illustrate the communication benefits of our method. The simulation results show that the number of transmitted bits can be reduced to 5-10% of the non-compressed method in the studied scenarios.