Regularization of non-homogeneous dynamic Bayesian networks with global information-coupling based on hierarchical Bayesian models

To relax the homogeneity assumption of classical dynamic Bayesian networks (DBNs), various recent studies have combined DBNs with multiple changepoint processes. The underlying assumption is that the parameters associated with time series segments delimited by multiple changepoints are a priori independent. Under weak regularity conditions, the parameters can be integrated out in the likelihood, leading to a closed-form expression of the marginal likelihood. However, the assumption of prior independence is unrealistic in many real-world applications, where the segment-specific regulatory relationships among the interdependent quantities tend to undergo gradual evolutionary adaptations. We therefore propose a Bayesian coupling scheme to introduce systematic information sharing among the segment-specific interaction parameters. We investigate the effect this model improvement has on the network reconstruction accuracy in a reverse engineering context, where the objective is to learn the structure of a gene regulatory network from temporal gene expression profiles. The objective of the present paper is to expand and improve an earlier conference paper in six important aspects. Firstly, we offer a more comprehensive and self-contained exposition of the methodology. Secondly, we extend the model by introducing an extra layer to the model hierarchy, which allows for information-sharing among the network nodes, and we compare various coupling schemes for the noise variance hyperparameters. Thirdly, we introduce a novel collapsed Gibbs sampling step, which replaces a less efficient uncollapsed Gibbs sampling step of the original MCMC algorithm. Fourthly, we show how collapsing and blocking techniques can be used for developing a novel advanced MCMC algorithm with significantly improved convergence and mixing. Fifthly, we systematically investigate the influence of the (hyper-)hyperparameters of the proposed model. Sixthly, we empirically compare the proposed global information coupling scheme with an alternative paradigm based on sequential information sharing.

Marco Grzegorczyk and Dirk Husmeier

Machine Learning 91 (1), 105-154