Variational inference for Dirichlet process mixtures

2006 · Bayesian Analysis · 1,489 citations · 4 from inside this corpus

Dirichlet process (DP) mixture models are the cornerstone of nonparametric Bayesian statistics, and the development of Monte-Carlo Markov chain (MCMC) sampling methods for DP mixtures has enabled the application of nonparametric Bayesian methods to a variety of practical data analysis problems. However, MCMC sampling can be prohibitively slow, and it is important to explore alternatives. One class of alternatives is provided by variational methods, a class of deterministic algorithms that convert inference problems into optimization problems (Opper and Saad 2001; Wainwright and Jordan 2003). Thus far, variational methods have mainly been explored in the parametric setting, in particular within the formalism of the exponential family (Attias 2000; Ghahramani and Beal 2001; Blei et al. 2003). In this paper, we present a variational inference algorithm for DP mixtures. We present experiments that compare the algorithm to Gibbs sampling algorithms for DP mixtures of Gaussians and present an application to a large-scale image analysis problem.

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What this paper cites, inside the corpus

Paper	Year	Cited
Latent dirichlet allocation	2003	27,078
A Bayesian Analysis of Some Nonparametric Problems	1973	4,833
An Introduction to Variational Methods for Graphical Models	1999	3,793
Graphical Models, Exponential Families, and Variational Inference	2007	3,171
Bayesian Density Estimation and Inference Using Mixtures	1995	2,248
Markov Chain Sampling Methods for Dirichlet Process Mixture Models	2000	2,217
Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems	1974	2,035
Variational Algorithms for Approximate Bayesian Inference	2003	1,736
A Constructive Definition of Dirichlet Priors	1991	1,612
Gibbs Sampling Methods for Stick-Breaking Priors	2001	1,568

What cites it, inside the corpus

Paper	Year	Cited
Variational Inference: A Review for Statisticians	2017	3,843
Graphical Models, Exponential Families, and Variational Inference	2007	3,171
Variational Inference: A Review for Statisticians	2023	2,169
Stochastic variational inference	2013	1,480

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Topics

Bayesian Methods and Mixture Models	Computer Science
Statistical Methods and Inference	Mathematics
Algorithms and Data Compression	Computer Science

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