Mean field analysis for Continuous Time Bayesian Networks

In this paper we investigate the use of the mean field technique to analyze Continuous Time Bayesian Networks (CTBN). They model continuous time evolving variables with exponentially distributed transition rates depending on the parent variables in the graph. CTBN inference consists of computing the probability distribution of a subset of variables, conditioned by the observation of other variables' values (evidence). The computation of exact results is often unfeasible due to the complexity of the model. For such reason, the possibility to perform the CTBN inference through the equivalent Generalized Stochastic Petri Net (GSPN) was investigated in the past. In this paper instead, we explore the use of mean field approximation and apply it to a well-known epidemic case study. The CTBN model is converted in both a GSPN and in a mean field based model. The example is then analyzed with both solutions, in order to evaluate the accuracy of the mean field approximation for the computation of the posterior probability of the CTBN given an evidence. A summary of the lessons learned during this preliminary attempt concludes the paper

Learning the structure of Bayesian Networks: A quantitative assessment of the effect of different algorithmic schemes

One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions, and by the fact that the problem is NP-hard. Hence, full enumeration of all the possible solutions is not always feasible and approximations are often required. However, to the best of our knowledge, a quantitative analysis of the performance and characteristics of the different heuristics to solve this problem has never been done before. For this reason, in this work, we provide a detailed comparison of many different state-of-the-arts methods for structural learning on simulated data considering both BNs with discrete and continuous variables, and with different rates of noise in the data. In particular, we investigate the performance of different widespread scores and algorithmic approaches proposed for the inference and the statistical pitfalls within them

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