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 prediction performance, as well as, 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：我们针对稀疏泊松回归模型问题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，将似然函数通过二次函数进行近似，从而获得该近似分量与回归系数高斯先验之间的共轭性。针对该问题采用了三种稀疏性增强先验。通过将所提模型相互比较，并与两种频率学派稀疏泊松方法（LASSO和SCAD）进行对比，评估了预测性能及所提方法的稀疏化性能。通过模拟数据示例，计算了变分贝叶斯方法相较于对应基准马尔可夫链蒙特卡洛方法的准确度。结果表明，所提变分贝叶斯方法为参数后验分布提供了良好近似，且变分贝叶斯方法的计算速度远快于马尔可夫链蒙特卡洛方法。利用多个基准计数响应数据集，在真实应用场景中评估了所提方法的预测性能。