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Abstract:
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A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being a mixture of Gaussian distribution. Although the Gaussian prior has shown to be suboptimal, we fi nd that with a Gaussian mixture and an adaptive choice on the Gaussian mean and mixture weights, we can show that the posterior distribution has the desirable asymptotic behavior, e.g., it concentrates on balls with the desired minimax rate. To achieve computation efficiency, we propose to obtain the posterior distribution by a deterministic variational algorithm. Empirical studies on several benchmark data sets demonstrate the superior performance of the proposed algorithm compared to other alternatives.
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