PCR/PLSR optimization based on noise covariance estimation and Kalman filtering theory

Abstract

The theoretical connection between principal component regression (PCR) and partial least squares regression (PLSR) on one hand and Kalman filtering (KF) on the other is known from earlier work. In the present paper we investigate the possibilities to use latent variables modeling and KF theory as means for optimization of ordinary PLSR and PCR predictors, based on the prerequisite of prior X noise covariance estimates facilitated e.g. by more X than y observations. The result is a new PLSR optimization method, while the PCR optimization turns out to be identical with an earlier known method. A simulation example and two real-world data examples supporting the theoretical development are presented. The treatment is limited to cases with only one response variable, although an extension to multiresponse cases is also possible.