Sparse Gaussian chain graphs with the spike-and-slab LASSO: Algorithms and asymptotics
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The Gaussian chain graph model simultaneously parametrizes (i) the direct effects of p predictors on q correlated outcomes and (ii) the residual partial covariance between pair of outcomes. We introduce a new method for fitting sparse Gaussian chain graph models with spike-and-slab LASSO (SSL) priors. We develop an Expectation-Conditional Maximization algorithm to obtain sparse estimates of the p × q matrix of direct effects and the q × q residual precision matrix. Our algorithm iteratively solves a sequence of penalized maximum likelihood problems with self-adaptive penalties that gradually filter out negligible regression coefficients and partial covariances. Because it adaptively penalizes model parameters, our method is seen to outperform fixed-penalty competitors on simulated data. We establish the posterior concentration rate for our model, buttressing our method's excellent empirical performance with strong theoretical guarantees. We use our method to reanalyze a dataset from a study of the effects of diet and residence type on the composition of the gut microbiome of elderly adults.
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