Open AccessProceedings Article
Matrix-Variate Dirichlet Process Mixture Models
Zhihua Zhang,Guang Dai,Michael I. Jordan +2 more
- pp 980-987
TLDR
A new Bayesian nonparametric model based on Dirichlet process priors that has advantages in both computational and statistical e‐ciency and makes use of a Markov chain Monte Carlo algorithm for inference and prediction.Abstract:
We are concerned with a multivariate response regression problem where the interest is in considering correlations both across response variates and across response samples. In this paper we develop a new Bayesian nonparametric model for such a setting based on Dirichlet process priors. Building on an additive kernel model, we allow each sample to have its own regression matrix. Although this overcomplete representation could in principle sufier from severe overfltting problems, we are able to provide efiective control over the model via a matrix-variate Dirichlet process prior on the regression matrices. Our model is able to share statistical strength among regression matrices due to the clustering property of the Dirichlet process. We make use of a Markov chain Monte Carlo algorithm for inference and prediction. Compared with other Bayesian kernel models, our model has advantages in both computational and statistical e‐ciency.read more
Citations
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Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95
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References
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Gaussian Processes for Machine Learning
TL;DR: The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics, and deals with the supervised learning problem for both regression and classification.
Journal ArticleDOI
A Bayesian Analysis of Some Nonparametric Problems
TL;DR: In this article, a class of prior distributions, called Dirichlet process priors, is proposed for nonparametric problems, for which treatment of many non-parametric statistical problems may be carried out, yielding results that are comparable to the classical theory.
Journal ArticleDOI
Bayesian Density Estimation and Inference Using Mixtures
Michael Escobar,Mike West +1 more
TL;DR: In this article, the authors describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes and show convergence results for a general class of normal mixture models.
Journal ArticleDOI
Markov Chain Sampling Methods for Dirichlet Process Mixture Models
TL;DR: In this article, Markov chain methods for sampling from the posterior distribution of a Dirichlet process mixture model are presented, and two new classes of methods are presented. But neither of these methods is suitable for handling general models with non-conjugate priors.