Controlling the false discoveries in LASSO

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.