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2016 Rate-adaptive Bayesian independent component analysis
Weining Shen, Jing Ning, Ying Yuan
Electron. J. Statist. 10(2): 3247-3264 (2016). DOI: 10.1214/16-EJS1183

Abstract

We consider independent component analysis (ICA) using a Bayesian approach. The latent sources are allowed to be block-wise independent while the underlying block structure is unknown. We consider prior distributions on the block structure, the mixing matrix and the marginal density functions of latent sources using a Dirichlet mixture and random series priors. We obtain a minimax-optimal posterior contraction rate of the joint density of the latent sources. This finding reveals that Bayesian ICA adaptively achieves the optimal rate of convergence according to the unknown smoothness level of the true marginal density functions and the unknown block structure. We evaluate the empirical performance of the proposed method by simulation studies.

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Weining Shen. Jing Ning. Ying Yuan. "Rate-adaptive Bayesian independent component analysis." Electron. J. Statist. 10 (2) 3247 - 3264, 2016. https://doi.org/10.1214/16-EJS1183

Information

Received: 1 December 2015; Published: 2016
First available in Project Euclid: 16 November 2016

zbMATH: 1359.62227
MathSciNet: MR3572848
Digital Object Identifier: 10.1214/16-EJS1183

Keywords: adaptive estimation , Dirichlet mixture prior , Independent component analysis , nonparametric Bayes , Posterior contraction rate

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 2 • 2016
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