Subspace information criterion for nonquadratic regularizers — Model selection for sparse regressors

Non-quadratic regularizers, in particular the ℓ1 norm regularizer can yield sparse solutions that generalize well. In this work we propose the Generalized Subspace Information Criterion (GSIC) that allows to predict the generalization error for this useful family of regularizers. We show that under some technical assumptions GSIC is an asymptotically unbiased estimator of the generalization error. GSICis demonstrated to have a good performance in experiments with the ℓ1 norm regularizer as we compare with the Network Information Criterion and cross-validation in relatively large sample cases. However in the small sample case, GSICtends to fail to capture the optimal model due to its large variance. Therefore, also a biased version of GSICis introduced, which achieves reliable model selection in the relevant and challenging scenario of high dimensional data and few samples. Subspace Information Criterion for Non-Quadratic Regularizers 2