🤖 AI Summary
To address substantial parameter estimation bias, low computational efficiency, and insufficient robustness in variable selection for sparse Poisson regression, this paper proposes the first non-conjugate variational Bayes (VB) inference framework tailored to this model. Methodologically, it introduces a quadratic approximation to the Poisson likelihood to restore conjugacy, enabling efficient closed-form updates; further, it integrates Laplace, Horseshoe, and Spike-and-Slab priors within a unified VB scheme to achieve adaptive sparsity-inducing variable selection. Compared to MCMC, the method accelerates computation by one to two orders of magnitude while ensuring small posterior approximation error and rapid convergence. Extensive experiments on synthetic and real-world count datasets demonstrate that the proposed approach significantly outperforms or matches state-of-the-art frequentist methods—including LASSO and SCAD—in estimation accuracy, predictive performance, and robust identification of sparse structures.
📝 Abstract
We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of 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. Throughout a simulated data example, the accuracy of the VB methods is computed compared to the corresponding benchmark MCMC methods. It can be observed that the proposed VB methods have provided a good approximation to the posterior distribution of the parameters, while the VB methods are much faster than the MCMC ones. Using several benchmark count response data sets, the prediction performance of the proposed methods is evaluated in real-world applications.
