A Review of Inference Algorithms for Hybrid Bayesian Networks

Hybrid Bayesian networks have received an increasing attention during the last years. The difference with respect to standard Bayesian networks is that they can host discrete and continuous variables simultaneously, which extends the applicability of the Bayesian network framework in general. However, this extra feature also comes at a cost: inference in these types of models is computationally more challenging and the underlying models and updating procedures may not even support closed-form solutions. In this paper we provide an overview of the main trends and principled approaches for performing inference in hybrid Bayesian networks. The methods covered in the paper are organized and discussed according to their methodological basis. We consider how the methods have been extended and adapted to also include (hybrid) dynamic Bayesian networks, and we end with an overview of established software systems supporting inference in these types of models

Who Learns Better Bayesian Network Structures: Accuracy and Speed of Structure Learning Algorithms

Three classes of algorithms to learn the structure of Bayesian networks from data are common in the literature: constraint-based algorithms, which use conditional independence tests to learn the dependence structure of the data; score-based algorithms, which use goodness-of-fit scores as objective functions to maximise; and hybrid algorithms that combine both approaches. Constraint-based and score-based algorithms have been shown to learn the same structures when conditional independence and goodness of fit are both assessed using entropy and the topological ordering of the network is known (Cowell, 2001). In this paper, we investigate how these three classes of algorithms perform outside the assumptions above in terms of speed and accuracy of network reconstruction for both discrete and Gaussian Bayesian networks. We approach this question by recognising that structure learning is defined by the combination of a statistical criterion and an algorithm that determines how the criterion is applied to the data. Removing the confounding effect of different choices for the statistical criterion, we find using both simulated and real-world complex data that constraint-based algorithms are often less accurate than score-based algorithms, but are seldom faster (even at large sample sizes); and that hybrid algorithms are neither faster nor more accurate than constraint-based algorithms. This suggests that commonly held beliefs on structure learning in the literature are strongly influenced by the choice of particular statistical criteria rather than just by the properties of the algorithms themselves.Comment: 27 pages, 8 figure

Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in solving a variety of hard control tasks. However, this new sophistication and extremely over-parameterized models have come with the cost of an overall reduction in our ability to interpret the resulting policies. In this paper, we take inspiration from the control community and apply the principles of hybrid switching systems in order to break down complex dynamics into simpler components. We exploit the rich representational power of probabilistic graphical models and derive an expectation-maximization (EM) algorithm for learning a sequence model to capture the temporal structure of the data and automatically decompose nonlinear dynamics into stochastic switching linear dynamical systems. Moreover, we show how this framework of switching models enables extracting hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts in an imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro