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Abstract:
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Graph-valued regression aims to study how graphical structures change with covariates. Nevertheless, there is a lack of statistical methods for graph-valued regression. Early proposed methods must first partition the space of covariates and then separately learn graphs on each portion of the data, resulting in unstable estimators and a loss of interpretability for the covariates. Recent emerging methods on the joint modeling of multiple graphical models can be viewed as a special case of graph-valued regression with the covariate being univariate and categorical. However, they cannot handle continuous covariates, let alone multiple covariates.
Here, based on Gaussian graphical models, we propose a novel Bayesian framework for graph-valued regression. Our proposed model can easily interpret the effects of covariates on each edge of the undirected graph, handle all types of covariates, and borrow strength across the whole covariate space to improve edge detection. We develop an efficient parallel Markov chain Monte Carlo algorithm to conduct posterior inference. We applied the proposed method to study how gene regulatory networks vary across different age and disease categories.
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