AbstractWe propose a new method for supervised learning, the “principal components lasso” (“pcLasso”). It combines the lasso (ℓ1) penalty with a quadratic penalty that shrinks the coefficient vector toward the feature matrix's leading principal components (PCs). pcLasso can be especially powerful if the features are preassigned to groups. In that case, pcLasso shrinks each group‐wise component of the solution toward the leading PCs of that group. The pcLasso method also carries out selection of feature groups. We provide some theory and illustrate the method on some simulated and real data examples.