Contrastive Principal Component Regression

Positive pairs reveal reproducible variation, but the most reproducible directions need not be the most predictive. We introduce contrastive principal component regression (C-PCR), which combines response association and pair alignment to learn a low-dimensional representation, then fits ridge regression for prediction from a single measurement. Under a paired-factor model, we characterize when this joint selection preserves a predictive direction that selection based only on reproducibility would discard. We derive a computable prediction-risk limit as feature dimension and sample size grow proportionally. With one predictive factor and one retained component, the scalar-response formula accounts for using the same responses in component selection and coefficient fitting. The formula separates predictive-direction error from accumulated error elsewhere. Simulations support it and demonstrate finite-sample prediction gains from combining pairing with supervision. Across five naturally paired spectroscopy datasets, our method achieves the best predictive performance or remains competitive with the best alternative.