Abstract

In this paper, we study the multinomial logistic regression with interactive effects. Our approach involves the implementation of the pliable lasso penalty which allows for estimating the main effects of the covariates X and an interaction effects between the covariates and a set modifiers Z. The hierarchical penalty helps to avoid over-fitting by excluding the interaction effects when the corresponding main effects are zero. The original log-likelihood model is transformed into an iteratively reweighted least square problem with the pliable lasso penalty and then, the block-wise coordinate descent approach is employed. Our results show that the pliable lasso for multinomial logistic regression has some good qualities and can perform well in multi-classification problems which involve interactive variables.

摘要

在本文中，我们研究了具有交互效应的多项逻辑回归。我们的方法涉及柔韧套索惩罚的实施，它允许估计协变量X的主要影响以及协变量和一组修饰符Z之间的交互效应. 当相应的主效应为零时，分层惩罚通过排除交互效应来帮助避免过度拟合。将原始对数似然模型转换为具有柔韧套索惩罚的迭代重新加权最小二乘问题，然后采用逐块坐标下降法。我们的结果表明，用于多项逻辑回归的柔韧套索具有一些良好的品质，并且可以在涉及交互变量的多分类问题中表现良好。