基于损失函数为指数平方形式的稳健Logistic回归

A Robust Logistic Regression with Exponential Squared Loss

Logistic回归模型在处理分类数据中有着十分广泛的应用,通常为了简化模型而使用Logit变换将模型化为线性回归模型,但Logit变换会导致误差分量分布函数不同,从而导致模型误差增大.首先对Logit变换进行修正,在考虑离群值影响的基础上,利用指数平方损失函数和自适应LASSO形式稳健回归惩罚函数,从而对线性回归模型进行了修正,其次对股票涨跌情况进行了预测,最后结果表明,修正的模型对期望风险较小的投资者有更高的预测成功率.

Logistic regression model in processing are widely used to handle classification data, in order to simplify the model, usually, Logit transform is used to convert it into the linear regression model, however, Logit transform can cause the differences of the error component distribution function, thereby increasing the model error. In the report, the Logit transform was modified, and based on the considering of the effects of outlier, the exponential squared loss function and adaptive LASSO penalty function were used to modify the linear regression model. Finally, the model was used to forecast the stock rose rate. The results indicated that for the expected risk small investors, the modified model have higher prediction success rate.