A Principal Components Approach to Combining Regression Estimates

The goal of combining the predictions of multiple learned models is to form an improved estimator. A combining strategy must be able to robustly handle the inherent correlation, or multicollinearity, of the learned models while identifying the unique contributions of each. A progression of existing approaches and their limitations with respect to these two issues are discussed. A new approach, PCR*, based on principal components regression is proposed to address these limitations. An evaluation of the new approach on a collection of domains reveals that (1) PCR* was the most robust combining method, (2) correlation could be handled without eliminating any of the learned models, and (3) the principal components of the learned models provided a continuum of “regularized” weights from which PCR* could choose.