Optimizing a vector of shrinkage factors for continuum regression

Abstract Continuum regression (CR) provides a promising regression framework encompassing ordinary least squares (OLS), partial least squares (PLS), and principal component regression (PCR). One important parameter of CR, namely shrinkage factor, determines how CR compromises between OLS and PCR. As the factor suggests, the rationale behind CR is that it aims at realizing a balance between achieving a good fit and establishing a stable model. However, traditional CR always uses a single shrinkage factor when extracting successive latent variables. As a consequence, the power of CR is surely limited. Aiming at this problem, we offer a vector of shrinkage factors for CR and one shrinkage factor for each latent variable. But now, identifying the optimal vector of shrinkage factors becomes a non-deterministic polynomial complete problem. As an effective optimization method, genetic algorithm (GA) is utilized to handle this tedious task. Together, the GACR framework is proposed in this study. The experiments on two real-world datasets illustrate the method’s applicability in practice.