Robust Elastic Net Regression

TL;DR

This paper introduces a robust elastic net (REN) model for high-dimensional sparse regression that enhances robustness against outliers by trimming inner products, with proven performance guarantees and superior experimental results.

Contribution

The paper proposes a novel robust elastic net model that incorporates trimming of inner products to improve robustness, along with theoretical guarantees and special cases like robust Lasso.

Findings

REN outperforms standard elastic net in robustness.

Theoretical bounds are established for statistical and optimization errors.

Experimental results confirm the effectiveness of the proposed method.

Abstract

We propose a robust elastic net (REN) model for high-dimensional sparse regression and give its performance guarantees (both the statistical error bound and the optimization bound). A simple idea of trimming the inner product is applied to the elastic net model. Specifically, we robustify the covariance matrix by trimming the inner product based on the intuition that the trimmed inner product can not be significant affected by a bounded number of arbitrarily corrupted points (outliers). The REN model can also derive two interesting special cases: robust Lasso and robust soft thresholding. Comprehensive experimental results show that the robustness of the proposed model consistently outperforms the original elastic net and matches the performance guarantees nicely.