📝 SummarXiv

Abstract

We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide an approximate conjugacy in the model, the likelihood is approximated by a quadratic function, which provides the conjugacy of the approximation component with the Gaussian prior on the regression coefficient. Three sparsity-enforcing priors are used for this problem. The proposed models are compared with each other and two frequentist sparse Poisson methods (LASSO and SCAD) to evaluate the estimation, prediction, and sparsity performance of the proposed methods. In a simulation study, the proposed VB methods closely approximate the posterior parameter distribution while achieving significantly faster computation than benchmark MCMC methods. Using several benchmark count response data sets, the prediction performance of the proposed methods is evaluated in real-world applications.