Stochastic matching pursuit for Bayesian variable selection |
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Authors: | Ray-Bing Chen Chi-Hsiang Chu Te-You Lai Ying Nian Wu |
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Institution: | 1.Institute of Statistics,National University of Kaohsiung,Kaohsiung,Taiwan;2.Department of Statistics,University of California,Los Angeles,USA |
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Abstract: | This article proposes a stochastic version of the matching pursuit algorithm for Bayesian variable selection in linear regression.
In the Bayesian formulation, the prior distribution of each regression coefficient is assumed to be a mixture of a point mass
at 0 and a normal distribution with zero mean and a large variance. The proposed stochastic matching pursuit algorithm is
designed for sampling from the posterior distribution of the coefficients for the purpose of variable selection. The proposed
algorithm can be considered a modification of the componentwise Gibbs sampler. In the componentwise Gibbs sampler, the variables
are visited by a random or a systematic scan. In the stochastic matching pursuit algorithm, the variables that better align
with the current residual vector are given higher probabilities of being visited. The proposed algorithm combines the efficiency
of the matching pursuit algorithm and the Bayesian formulation with well defined prior distributions on coefficients. Several
simulated examples of small n and large p are used to illustrate the algorithm. These examples show that the algorithm is efficient for screening and selecting variables. |
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