A study on tuning parameter selection for the high-dimensional lasso

Abstract

High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by tuning parameters, is integral to achieving good performance. One can choose the tuning parameter in a variety of ways, such as through resampling methods or generalized information criteria. However, the theory supporting many regularized procedures relies on an estimate for the variance parameter, which is complicated in high dimensions. We develop a suite of information criteria for choosing the tuning parameter in lasso regression by leveraging the literature on high-dimensional variance estimation. We derive intuition showing that existing information-theoretic approaches work poorly in this setting. We compare our risk estimators to existing methods with an extensive simulation and derive some theoretical justification. We find that our new estimators perform well across a wide range of simulation conditions and evaluation criteria.

64 pages, 11 figures

References in corpus (6)

• On the "degrees of freedom" of the lasso
• Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection
• Tuning parameter selection in high dimensional penalized likelihood
• Sparsity oracle inequalities for the Lasso
• Sparse Matrix Inversion with Scaled Lasso
• Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models

Cited by in corpus (1)

• Thresholding Greedy Pursuit for Sparse Recovery Problems