We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding conjugacy between the approximation component and the Gaussian prior on the regression coefficient. Three sparsity-enforcing priors (Laplace, Continuous Spike and Slab, and Bernoulli) are used for this problem. The proposed models are compared with each other, the associated MCMC models, and two frequentist sparse Poisson methods (LASSO and SCAD) to evaluate their estimation, prediction, and sparsity performance. 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.

翻译：针对稀疏泊松回归模型问题，我们采用了非共轭变分贝叶斯方法。为在模型中提供近似共轭性，似然函数通过二次函数进行近似，使得近似部分与回归系数的高斯先验之间形成共轭关系。该问题中使用了三种增强稀疏性的先验分布（拉普拉斯先验、连续钉板先验和伯努利先验）。所提出的模型相互之间、与相应的MCMC模型、以及两种频率学派稀疏泊松方法（LASSO和SCAD）进行比较，以评估其估计性能、预测性能和稀疏性表现。在模拟研究中，所提出的变分贝叶斯方法能够紧密逼近后验参数分布，同时计算速度显著快于基准MCMC方法。通过使用多个基准计数响应数据集，在现实应用中评估了所提出方法的预测性能。