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Sparse Bayesian Lasso via a Variable-Coefficient $\ell_1$ Penalty by Wycoff, Nathan; Arab, Ali; Donato, Katharine M.; Singh, Lisa O. is a scholarly article available to read on EtoBox.

What is Sparse Bayesian Lasso via a Variable-Coefficient $\ell_1$ Penalty about?

Modern statistical learning algorithms are capable of amazing flexibility, but struggle with interpretability. One possible solution is sparsity: making inference such that many of the parameters are estimated as being identically 0, which may be imposed through the use of nonsmooth penalties such as the $\ell_1$ penalty. However, the $\ell_1$ penalty introduces significant bias when high sparsity is desired. In this article, we retain the $\ell_1$ penalty, but define learnable penalty weights $\lambda_p$ endowed with hyperpriors. We start the article by investigating the optimization problem this poses, developing a proximal operator associated with the $\ell_1$ norm. We then study the theoretical properties of this variable-coefficient $\ell_1$ penalty in the context of penalized likelihood. Next, we investigate application of this penalty to Variational Bayes, developing a model we call the Sparse Bayesian Lasso which allows for behavior qualitatively like Lasso regression to be applied to arbitrary variational models. In simulation studies, this gives us the Uncertainty Quantification and low bias properties of simulation-based approaches with an order of magnitude less computa

Author

Wycoff, Nathan; Arab, Ali; Donato, Katharine M.; Singh, Lisa O.

Published

2022

Language

EN