Cluster Variational Approximations for Structure Learning of Continuous-Time Bayesian Networks from Incomplete Data

TL;DR

This paper introduces a cluster-variational approximation method for structure learning in continuous-time Bayesian networks, enabling scalable analysis from incomplete and noisy data, and surpassing existing techniques in efficiency.

Contribution

The authors develop a novel cluster-variational approach that improves scalability and accuracy for structure learning in CTBNs with incomplete data, building on recent statistical physics methods.

Findings

Outperforms existing methods in scalability

Effectively handles incomplete and noisy data

Analytically marginalizes secondary parameters

Abstract

Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among interacting entities. However, if the available data is incomplete, one needs to simulate the prohibitively complex CTBN dynamics. Existing approximation techniques, such as sampling and low-order variational methods, either scale unfavorably in system size, or are unsatisfactory in terms of accuracy. Inspired by recent advances in statistical physics, we present a new approximation scheme based on cluster-variational methods significantly improving upon existing variational approximations. We can analytically marginalize the parameters of the approximate CTBN, as these are of secondary importance for structure learning. This recovers a scalable scheme for direct structure learning from incomplete and noisy time-series data. Our approach outperforms existing methods in terms of scalability.