Partial least trimmed squares regression

Abstract

Partial least squares (PLS) regression is a linear regression technique and plays an important role in dealing with high-dimensional regressors. Unfortunately, PLS is sensitive to outliers in datasets and consequentially produces a corrupted model. In this paper, we propose a robust method for PLS based on the idea of least trimmed squares (LTS), in which the objective is to minimize the sum of the smallest h squared residuals. However, solving an LTS problem is generally NP-hard. Inspired by the complementary idea of Sim and Hartley, we solve the inverse of the LTS problem instead and formulate it as a concave maximization problem, which is convex and can be solved in polynomial time. Classic PLS as well as two of the most efficient robust PLS methods, Partial Robust M (PRM) regression and RSIMPLS, are compared in this study. Results of both simulation and real data sets show the effectiveness and robustness of our approach.