A0773
Title: A variational inference approach to variable selection for heteroskedastic regression models
Authors: Giulia Livieri - The London School of Economics and Political Science (United Kingdom) [presenting]
Mauro Bernardi - University of Padova (Italy)
Luca Maestrini - The Australian National University (Australia)
Abstract: Variable selection plays a key role in modern statistical research and learning. Major classes of variable selection approaches are implemented using Markov chain Monte Carlo methods. These methods may be computationally impractical for large-scale problems or complex models, and faster approximations are desirable or necessary. An approach to variable selection is developed for heteroscedastic regression models based upon semiparametric mean field variational Bayes. The proposed methodology is suitable for models having linear mean and exponential variance functions with prior specifications that induce sparse solutions on the regression coefficients. The use of classic mean field variational Bayes leads to the approximating densities having non-standard forms, and challenging numerical problems arise in the determination of the optimal approximation. Tractability is achieved by imposing a parametric assumption to the approximate marginal posterior densities of variance regression coefficients. The iterative optimization of the log-likelihood lower bound includes Newton-type steps with analytical derivative expressions for the parametric component of the approximation. This optimization strategy uses new results that solve recurrent issues of constrained optimization involving multivariate skew-normal variational approximations. Illustrations demonstrate the approach is computationally efficient and accurate in comparison to Markov chain Monte Carlo.
