An approximate maximum likelihood interpretation of partial least squares (PLS) S. Co. 2013 Conference

Abstract

Partial Least Squares (PLS) is a popular regularization method in multiple regression. Although PLS has been used successfully as an algorithm for many years, its statistical interpretation is still not widely appreciated. The aim of this paper is to consolidate and extend results in the literature to (a) show that PLS estimation can be regarded as estimation under a statistical model based on the so-called the “Krylov hypothesis”,(b) introduce a derivation of the PLS estimator as approximate maximum likelihood estimator under this model and (c) propose an algorithm to modify the PLS estimator to yield the proper maximum likelihood estimator.