Abstract: In engineering applications, such as data mining, cost prediction, risk prediction etc., Logistic regression is a class of very important prediction methods. Presently, most of Logistic regression methods are designed based on optimization criteria, and these methods have several shortcomings such as tedious parameter tuning, poor model interpretation, and with the estimator no confidence interval. Therefore, we study the modeling and inference problem of Logistic group sparse regression from the perspective of Bayesian probability in this paper. Specifically, a Bayesian probability model of Logistic group sparse regression is firstly proposed by using the Gaussian-variance mixture formula. Then, an efficient inference algorithm is designed through the variational Bayesian method. Numerical results on simulated data show that the proposed method has better prediction performance.

Key words: Bayesian method, group sparse, variational inference, Logistic regression model