Two Bayesian Approaches to Dynamic Gaussian Bayesian Networks with Intra- and Inter-Slice Edges

TL;DR

This paper compares two Bayesian methods for learning Gaussian Dynamic Bayesian Networks with complex intra- and inter-slice dependencies, revealing distinct equivalence classes and proposing a new algorithm for structure identification.

Contribution

It introduces a comparison of mBGe and eBGe models for GDBNs, highlighting their different equivalence classes and proposing a novel DAG-to-CPDAG algorithm for non-standard classes.

Findings

The two models induce different network structure equivalence classes.

eBGe model's equivalence classes are non-standard and previously unreported.

A new DAG-to-CPDAG algorithm is proposed for identifying these classes.

Abstract

Gaussian Dynamic Bayesian Networks (GDBNs) are a widely used tool for learning network structures from continuous time-series data. To capture both time-lagged and contemporaneous dependencies, advanced GDBNs allow for dynamic inter-slice edges as well as static intra-slice edges. In the literature, two Bayesian modeling approaches have been developed for GDBNs. Both build on and extend the well-known Gaussian BGe score. We refer to them as the mean-adjusted BGe (mBGe) and the extended BGe (eBGe) models. In this paper, we contrast the two models and compare their performance empirically. The main finding of our study is that the two models induce different equivalence classes of network structures. In particular, the equivalence classes implied by the eBGe model are non-standard, and we propose a new variant of the DAG-to-CPDAG algorithm to identify them. To the best of our knowledge, these non-standard equivalence classes have not been previously reported.