Covariate-Assisted Bayesian Graph Learning for Heterogeneous Data

1889 

Contributed Abstract 

Paper 

Yabo Niu (1), Yang Ni (2), Debdeep Pati (2), Bani Mallick (2)

(1) University of Houston, N/A, (2) Texas A&M University, N/A

Yang Ni  
Texas A&M University

Debdeep Pati  
Texas A&M University

Bani Mallick  
Texas A&M University

Yabo Niu  
University of Houston

Yabo Niu  
University of Houston

In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets under-utilized in determining the joint dependency structure. In this talk, we consider a Bayesian approach to model undirected graphs underlying heterogeneous multivariate observations with additional assistance from covariates. Building on product partition models, we propose a novel covariate-dependent Gaussian graphical model that allows graphs to vary with covariates so that observations whose covariates are similar share a similar undirected graph. To efficiently embed Gaussian graphical models into our proposed framework, we explore both Gaussian likelihood and pseudo-likelihood functions. Moreover, the proposed model has large prior support. We show that based on the theory of fractional likelihood, the rate of posterior contraction is minimax optimal. The efficacy of the approach is demonstrated via simulation studies and an analysis of a protein network for a breast cancer dataset assisted by mRNA gene expression as covariates.

product partition model|Gaussian graphical model|pseudo-likelihood|G-Wishart prior|posterior contraction rate|

Section on Bayesian Statistical Science

Bayesian nonparametrics