基于预测校正算法的Spike and Slab Lasso逻辑回归模型

The Spike and Slab Lasso Logistic Regression Model Based on Prediction Correction Algorithm

摘要: 尽管Spike and Slab方法广泛应用于贝叶斯变量选择，但其惩罚似然估计的潜力在很大程度上被忽视了。通过在贝叶斯模态中引入惩罚化似然观点，本文提出了新的Spike and Slab Lasso逻辑回归模型，将两个拉普拉斯密度的混合先验置于单个坐标上，可以自适应地收缩系数，即弱收缩重要预测量，强收缩不相关预测量，从而可以得到准确的估计和预测。同时，我们使用了预测–校正算法来求解Spike and Slab Lasso逻辑回归模型，并将该算法扩展到不可分离惩罚的情况。该算法利用凸优化的预测校正算法，沿着整个正则化路径有效的计算解，方便了模型选择，避免了正则化参数值不同时的独立优化。最后，模拟学习和实证结果表明本文所提模型比Lasso逻辑回归模型具有更优的性能。

Abstract: Although the Spike and Slab method is widely used in Bayesian variable selection, its potential for penalized likelihood estimation is ignored. By introducing the penalized likelihood into the Bayes-ian case, this paper proposes a new Spike and Slab Lasso logistic regression model, which places the mixed priors of two Laplace densities on a single coordinate, and can adaptively adjust the shrink-age coefficient, that is, the weak shrinkage important predictor and the strong shrinkage irrelevant predictor, so that accurate estimation and prediction can be obtained. At the same time, we use the prediction-correction algorithm for the Spike and Slab Lasso logistic regression model, and extend the algorithm to the case of non-separable penalty. The algorithm uses the prediction correction algorithm of convex optimization to effectively calculate the solution along the entire regularization path, which facilitates model selection and avoids independent optimization when the regulariza-tion parameter values are different. Finally, the simulation learning and empirical results show that the proposed model has better performance than lasso logistic regression model.