Discovering the Hidden Structure of Complex Dynamic Systems

Dynamic Bayesian networks provide a compact and natural representation for complex dynamic systems. However, in many cases, there is no ex­ pert available from whom a model can be elicited. Learning provides an alternative approach for constructing models of dynamic systems. In this paper, we address some of the crucial compu­ tational aspects of learning the structure of dy­ namic systems, particularly those where some relevant variables are partially observed or even entirely unknown. Our approach is based on the Structural Expectation Maximization (SEM) al­ gorithm. The main computational cost of the SEM algorithm is the gathering of expected suf­ ficient statistics. We propose a novel approxima­ tion scheme that allows these sufficient statistics to be computed efficiently. We also investigate the fundamental problem of discovering the exis­ tence of hidden variables without exhaustive and expensive search. Our approach is based on the observation that, in dynamic systems, ignoring a hidden variable typically results in a violation of the Markov property. Thus, our algorithm searches for such violations in the data, and in­ troduces hidden variables to explain them. We provide empirical results showing that the algo­ rithm is able to learn the dynamics of complex systems in a computationally tractable way.