Using the Krylov Subspace Formulation to Improve Regularisation and Interpretation in Partial Least Squares Regression
Abstract: Partial least squares regression (PLS-R) has been an important regression method in the life sciences and many other fields for decades. However, PLS-R is typically solved using an algorithmic approach, rather than through an optimisation formulation and procedure. There is a clear optimisation formulation of the PLS-R problem based on a Krylov subspace formulation, but it is only rarely considered. The popularity of PLS-R is attributed to the ability to interpret the data through the model components, but the model components are not available when solving the PLS-R problem using the Krylov subspace formulation. We therefore highlight a simple reformulation of the PLS-R problem using the Krylov subspace formulation as a promising modelling framework for PLS-R, and illustrate one of the main benefits of this reformulation---namely that it allows arbitrary penalty terms of the regression coefficients to be included in the PLS-R model. Further, we propose an approach to estimate the PLS-R model components for the solution found through the Krylov subspace formulation, that are those we would have obtained had we been able to use the common algorithms for estimating the PLS-R model. We illustrate the utility of the proposed method on simulated and real data.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Ruoyu_Sun1
Submission Number: 200
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