On The Sparse Bayesian Learning Of Linear Models

Yves Atchade; Chia Chye Yee

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arXiv · 1502.03416

On The Sparse Bayesian Learning Of Linear Models

Yves Atchade·Chia Chye Yee

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Abstract

This work is a re-examination of the sparse Bayesian learning (SBL) of linear regression models of Tipping (2001) in a high-dimensional setting. We propose a hard-thresholded version of the SBL estimator that achieves, for orthogonal design matrices, the non-asymptotic estimation error rate of $\sigma\sqrt{s\log p}/\sqrt{n}$, where $n$ is the sample size, $p$ the number of regressors, $\sigma$ is the regression model standard deviation, and $s$ the number of non-zero regression coefficients. We also establish that with high-probability the estimator identifies the non-zero regression coefficients. In our simulations we found that sparse Bayesian learning regression performs better than lasso (Tibshirani (1996)) when the signal to be recovered is strong.

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Yves Atchade, Chia Chye Yee. 2015-02-11. On The Sparse Bayesian Learning Of Linear Models. https://arxiv.org/abs/1502.03416

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