We have utilized the non-conjugate VB method for the problem of the sparse Poisson regression model. To provide an approximated conjugacy in the model, the likelihood is approximated by a quadratic function, which provides the conjugacy of the approximation component with the Gaussian prior to 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 the sparsing 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.

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，这使得近似分量与回归系数的高斯先验形成共轭关系。该问题中使用了三种促进稀疏性的先验分布。所提出的模型相互比较，并与两种频率学派稀疏泊松方法（LASSO和SCAD）进行对比，以评估所提方法在参数估计、预测及稀疏化性能方面的表现。通过模拟数据示例，计算了变分贝叶斯方法相对于对应基准马尔可夫链蒙特卡罗方法的精度。可以观察到，所提出的变分贝叶斯方法对参数后验分布提供了良好近似，同时其计算速度远快于马尔可夫链蒙特卡罗方法。基于多个基准计数响应数据集，在现实应用中评估了所提方法的预测性能。