Variable Selection via Basis Pursuit for Non-Gaussian Data

A simultaneous flexible variable selection procedure is proposed by applying a basis pursuit method to the likelihood function. The basis functions are chosen to be compatible with variable selection in the context of smoothing spline ANOVA models. Since it is a generalized LASSO-type method, it enjoys the favorable property of shrinking coefficients and gives interpretable results. We derive a Generalized Approximate Cross Validation function (GACV), an approximate leave-out-one cross validation function used to choose smoothing parameters. In order to apply the GACV function for a large data set situation, we propose a corresponding randomized GACV. A technique called ‘slice modeling’ is used to develop an efficient code. Our simulation study shows the effectiveness of the proposed approach in the Bernoulli case.