Robust and Sparse Multinomial Regression in High Dimensions

TL;DR

This paper introduces a robust and sparse multinomial regression estimator suitable for high-dimensional data, combining trimming for robustness and elastic net penalty for sparsity, extending previous linear and logistic models.

Contribution

It extends the enet-LTS estimator to multinomial regression, providing an algorithm and demonstrating improved robustness and sparsity in high-dimensional settings.

Findings

The estimator outperforms non-robust methods in simulations.

Real data examples show practical usefulness.

The algorithm effectively computes the estimator.

Abstract

A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty, which is a mixture of $L_1$ and $L_2$ penalties. From this point of view, the proposed estimator is an extension of the enet-LTS estimator \citep{Kurnaz18} for linear and logistic regression to the multinomial regression setting. After introducing an algorithm for its computation, a simulation study is conducted to show the performance in comparison to the non-robust version of the multinomial regression estimator. Some real data examples underline the usefulness of this robust estimator.