Scalable Structure Learning of Continuous-Time Bayesian Networks from Incomplete Data

Abstract

Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if data is incomplete, the latent states of the CTBN have to be estimated by laboriously simulating the intractable dynamics of the assumed CTBN. This is a problem, especially for structure learning tasks, where this has to be done for each element of a super-exponentially growing set of possible structures. In order to circumvent this notorious bottleneck, we develop a novel gradient-based approach to structure learning. Instead of sampling and scoring all possible structures individually, we assume the generator of the CTBN to be composed as a mixture of generators stemming from different structures. In this framework, structure learning can be performed via a gradient-based optimization of mixture weights. We combine this approach with a new variational method that allows for a closed-form calculation of this mixture marginal likelihood. We show the scalability of our method by learning structures of previously inaccessible sizes from synthetic and real-world data.

DYNOTEARS: Structure Learning from Time-Series Data

“…In this paper, we revisit the problem of learning dynamic Bayesian networks (DBNs) (Dean and Kanazawa, 1989;Murphy, 2002) from data. DBNs have been used successfully in a variety of domains such as clinical disease prognosis (Van Gerven et al, 2008;Zandonà et al, 2019), gene regulatory network (Linzner et al, 2019), facial and speech recognition (Meng et al, 2019;Nefian et al, 2002), neuroscience (Rajapakse and Zhou, 2007), among others. DBNs are the standard approach to modeling discrete-time temporal dynamics in directed graphical models.…”