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Activity Number: 244
Type: Contributed
Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #315100
Title: On the Sparse Bayesian Learning of Linear Models
Author(s): Chia Chye Yee* and Yves Atchade
Companies: University of Michigan and University of Michigan
Keywords: High-dimensional Regression ; Sparse ; Bayes ; EM algorithm ; LASSO
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 the non- asymptotic estimation error rate of \sqrt{slog p \over 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 (Tibshirani (1996)) when the signal to be recovered is strong.


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