Structure learning of Bayesian networks involving cyclic structures

TL;DR

This paper introduces a novel approach to model cyclic biological networks within Bayesian networks by embedding cycles as multivariate nodes, enabling structure learning with MCMC methods.

Contribution

It proposes a new model that incorporates cyclic structures into Bayesian networks, overcoming the acyclicity constraint and allowing for effective inference in biological networks.

Findings

Enables modeling of cyclic biological networks within Bayesian frameworks.

Uses MCMC for inference on the posterior distribution of graph structures.

Demonstrates the approach in the linear Gaussian case.

Abstract

Many biological networks include cyclic structures. In such cases, Bayesian networks (BNs), which must be acyclic, are not sound models for structure learning. Dynamic BNs can be used but require relatively large time series data. We discuss an alternative model that embeds cyclic structures within acyclic BNs, allowing us to still use the factorization property and informative priors on network structure. We present an implementation in the linear Gaussian case, where cyclic structures are treated as multivariate nodes. We use a Markov Chain Monte Carlo algorithm for inference, allowing us to work with posterior distribution on the space of graphs.