A0643
Title: Covariate-assisted Bayesian graph learning for heterogeneous data
Authors: Yabo Niu - University of Houston (United States) [presenting]
Yang Ni - Texas A&M University (United States)
Debdeep Pati - Texas A&M University (United States)
Bani Mallick - Texas A&M University (United States)
Abstract: In traditional Gaussian graphical models, data homogeneity is routinely assumed with no extra variables affecting conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets under-utilized in determining the joint dependency structure. A new Bayesian approach is presented to model undirected graphs underlying heterogeneous multivariate observations with additional assistance from covariates. Building on product partition models, a novel covariate-dependent Gaussian graphical model is proposed 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 the proposed framework, both Gaussian likelihood and pseudo-likelihood functions are explored. Moreover, the proposed model induced by the prior has large support and is flexible to approximate any piece-wise constant conditional variance-covariance matrices. Furthermore, based on the theory of fractional likelihood, the rate of posterior contraction is minimax optimal, assuming the true density is a Gaussian mixture with a known number of components. The efficacy of the approach is demonstrated via numerical studies and analysis of protein networks for a breast cancer dataset assisted by genetic covariates.
