Controlling the false discoveries in LASSO

Abstract

The LASSO method estimates coefficients by minimizing the residual sum of squares plus a penalty term. The regularization parameter λ in LASSO controls the trade-off between data fitting and sparsity. We derive relationship between λ and the false discovery proportion (FDP) of LASSO estimator and show how to select λ so as to achieve a desired FDP. Our estimation is based on the asymptotic distribution of LASSO estimator in the limit of both sample size and dimension going to infinity with fixed ratio. We use a factor analysis model to describe the dependence structure of the design matrix. An efficient majorization–minimization based algorithm is developed to estimate the FDP at fixed value of λ. The analytic results are compared with those of numerical simulations on finite-size systems and are confirmed to be correct. An application to the high-throughput genomic riboavin data set also demonstrates the usefulness of our method.