Department of Statistics
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Chia Chye Yee
PhD student, Department of Statistics, University of Michigan
On the sparse Bayesian Learning of linear models
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 the non-asymptotic estimation error rate of $\sqrt{s\log p}/\sqrt{n}$, where $n$ is the sample size, $p$ the number of regressors 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 (Tibshiranin 1996) when the signal to be recovered is strong.
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