Directed Cyclic Graph learning using covariate via MCMC

Music City Center 

Discovering graph structures with cycles from covariate-rich, heterogeneous datasets has been a very challenging and less studied problem. Most of the existing works predominantly centered around learning directed acyclic graphs (DAGs) or undirected graphs in such setup which may be too restrictive for practical implementations. In this article, we propose Bayesian covariate dependent Directed Cyclic Graph model (DCGx) which uses structural equation modelling. Our method allows to learn the underlying cyclic graphs which smoothly vary with covariates by utilizing covariate dependent partition model. For posterior inference we develop parallel tempered Markov Chain Monte Carlo (MCMC) sampler which ensures the eigen condition is satisfied for each covariate dependent cyclic graph. We demonstrate the ability of the proposed algorithm through extensive simulation studies and application to spatial transcriptomics dataset from dorsolateral prefrontal cortex (DLPFC) in human brains where the cell locations serve as the covariates.

Directed cyclic graphs

Covariate dependent partition model

Parallel Tempering

MCMC

Covariate dependent graphs 

Section on Bayesian Statistical Science