Hedging parameter selection for basis pursuit

Stephane Chretien; Alex Gibberd; Sandipan Roy

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arXiv · 1805.01870

Hedging parameter selection for basis pursuit

Stephane Chretien·Alex Gibberd·Sandipan Roy

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Abstract

In Compressed Sensing and high dimensional estimation, signal recovery often relies on sparsity assumptions and estimation is performed via $\ell_1$-penalized least-squares optimization, a.k.a. LASSO. The $\ell_1$ penalisation is usually controlled by a weight, also called "relaxation parameter", denoted by $\lambda$. It is commonly thought that the practical efficiency of the LASSO for prediction crucially relies on accurate selection of $\lambda$. In this short note, we propose to consider the hyper-parameter selection problem from a new perspective which combines the Hedge online learning method by Freund and Shapire, with the stochastic Frank-Wolfe method for the LASSO. Using the Hedge algorithm, we show that a our simple selection rule can achieve prediction results comparable to Cross Validation at a potentially much lower computational cost.

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Stephane Chretien, Alex Gibberd, Sandipan Roy. 2018-05-04. Hedging parameter selection for basis pursuit. https://arxiv.org/abs/1805.01870

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