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In modern data analysis, there is an increasing availability of datasets with numerous variables. Linear models that deal with abundant predictor variables often have poor performance because they tend to produce large variances. As well known, partial least squares (PLS) regression standouts because it is serviceable even if the number of variables far exceeds the number of samples. However, PLS, at its core, is a least‐squares method based on latent space, which is spanned by the components extracted from the original predictors. Hence, it is sensitive to outliers. In this study, incorporating the idea of least median of squares, we propose a new robust PLS method, namely, partial least median of squares (PLMS) regression. Unlike most of the robust counterparts, we solve the PLMS problem via modern optimization rather than a heuristic process or a reweighting strategy. A classical PLS method and two of the most efficient robust PLS methods are compared with our method. Results on simulations and two real‐world data sets demonstrate the effectiveness and robustness of our approach. Outliers are no exception in modern data analysis. In this study, incorporating the idea of least median of squares, we propose a new robust partial least squares method, namely, partial least median of squares (PLMS) regression. Unlike most of its robust counterparts, we solve the PLMS problem via modern optimization rather than a heuristic process or a reweighting strategy. Results on simulations and two real‐world datasets demonstrate the effectiveness and robustness of our approach. [ABSTRACT FROM AUTHOR]

Partial least squares (PLS) performs well for high-dimensional regression problems, where the number of predictors can far exceed the number of observations. Similar to many other supervised learning techniques, PLS was developed in the framework of empirical risk minimization, which typically assumes that the test and training data are drawn from the same distribution. Any violation of this assumption can deteriorate the PLS performance. Subsampling via an influence function is a recently developed and promising technique for addressing this problem. However, influence functions are only guaranteed to be accurate for sufficiently small changes to the model, limiting their application to small-scale datasets. To overcome this obstacle, a new form of the influence function for PLS is derived, and a framework of subsampling via an influence function for PLS is developed. Compared with the classic PLS and two other subsampling frameworks, the results on four simulation datasets and two real-world datasets illustrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

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. • A new robust method for partial least squares is introduced, combining with the idea of least trimmed squares. • The robust method is realized via modern optimization. • Results of simulation and real-world datasets show the effectiveness of our method. [ABSTRACT FROM AUTHOR]