Estimating sparse direct effects in multivariate regression with the spike-and-slab LASSO
Bayesian Analysis(2022)
摘要
The Gaussian chain graph model simultaneously parametrizes (i) the direct
effects of p predictors on q outcomes and (ii) the residual partial
covariances between pairs 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 individual model parameters, our
method is seen to outperform fixed-penalty competitors on simulated data. We
establish the posterior contraction rate for our model, buttressing our
method's excellent empirical performance with strong theoretical guarantees.
Using our method, we estimated the direct effects of diet and residence type on
the composition of the gut microbiome of elderly adults.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要