Logistic 组稀疏回归模型的 Bayes 建模及变分推断

在工程应用中，如数据挖掘、成本预测以及风险预测等，Logistic 回归是一类十分重要的预测方法．当前，大部分 Logistic 回归方法都是基于优化准则而设计，这类回归方法具有参数调试过程繁琐、模型解释性差、估计子没有置信区间等缺点．本文从 Bayes 概率角度研究 Logistic 组稀疏性回归的建模与推断问题．具体来说，首先利用高斯-方差混合公式提出 Logistic 组稀疏回归的 Bayes 概率模型；其次，通过变分 Bayes 方法设计出一个高效的推断算法．在模拟数据上的实验结果表明，本文所提出的方法具有较好的预测性能．

Bayesian Modeling and Variational Inference for Logistic Group Sparse Regression Model

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.