Bayesian Empirical Likelihood with Dual Penalties for Variable Selection in Ultra-high Dimensional Data
Conference
64th ISI World Statistics Congress - Ottawa, Canada
Format: IPS Abstract
Session: IPS 202 - Advances in Bayesian Hierarchical Modeling and Variable Selection for Complex Data
Tuesday 18 July 2 p.m. - 3:40 p.m. (Canada/Eastern)
Abstract
In the semi-parametric domain, under the ultra-high dimensional setting, we propose a Bayesian empirical likelihood method for variable selection, which requires no distributional assumptions but only estimating equations. Motivated by Chang et al. (2018) on doubly penalized empirical likelihood (EL), we introduce priors to regularize both regression parameters and Lagrange multipliers associated with the estimating equations, to promote sparse learning. We show theoretically that the posterior consistency and the variable selection consistency are ensured under some mild conditions. We further develop an efficient Markov chain Monte Carlo (MCMC) sampling algorithm based on the active set idea, which has been proved to be useful in reducing computational burden.