Math @ Duke

Publications [#257966] of David B. Dunson
search www.stat.duke.edu.Papers Published
 Bhattacharya, A; Dunson, DB, Sparse Bayesian infinite factor models.,
Biometrika, vol. 98 no. 2
(June, 2011),
pp. 291306, ISSN 00063444 [23049129], [doi]
(last updated on 2018/02/19)
Abstract: We focus on sparse modelling of highdimensional covariance matrices using Bayesian latent factor models. We propose a multiplicative gamma process shrinkage prior on the factor loadings which allows introduction of infinitely many factors, with the loadings increasingly shrunk towards zero as the column index increases. We use our prior on a parameterexpanded loading matrix to avoid the order dependence typical in factor analysis models and develop an efficient Gibbs sampler that scales well as data dimensionality increases. The gain in efficiency is achieved by the joint conjugacy property of the proposed prior, which allows block updating of the loadings matrix. We propose an adaptive Gibbs sampler for automatically truncating the infinite loading matrix through selection of the number of important factors. Theoretical results are provided on the support of the prior and truncation approximation bounds. A fast algorithm is proposed to produce approximate Bayes estimates. Latent factor regression methods are developed for prediction and variable selection in applications with highdimensional correlated predictors. Operating characteristics are assessed through simulation studies, and the approach is applied to predict survival times from gene expression data.


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