Variational inference for Dirichlet process mixtures
David M. Blei, Michael I. Jordan
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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- Variational Inference: A Review for Statisticians→Variational inference for Dirichlet process mixturesLegacy edge — source detail unavailable
- Graphical Models, Exponential Families, and Variational Inference→Variational inference for Dirichlet process mixturesLegacy edge — source detail unavailable
- Variational Inference: A Review for Statisticians→Variational inference for Dirichlet process mixturesLegacy edge — source detail unavailable
- Stochastic variational inference→Variational inference for Dirichlet process mixturesLegacy edge — source detail unavailable
- Variational inference for Dirichlet process mixtures→Latent dirichlet allocationLegacy edge — source detail unavailable
- Variational inference for Dirichlet process mixtures→A Bayesian Analysis of Some Nonparametric ProblemsLegacy edge — source detail unavailable
- Variational inference for Dirichlet process mixtures→An Introduction to Variational Methods for Graphical ModelsLegacy edge — source detail unavailable
- Variational inference for Dirichlet process mixtures→Graphical Models, Exponential Families, and Variational InferenceLegacy edge — source detail unavailable
- Variational inference for Dirichlet process mixtures→Bayesian Density Estimation and Inference Using MixturesLegacy edge — source detail unavailable
- Variational inference for Dirichlet process mixtures→Markov Chain Sampling Methods for Dirichlet Process Mixture ModelsLegacy edge — source detail unavailable
- Variational inference for Dirichlet process mixtures→Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric ProblemsLegacy edge — source detail unavailable
- Variational inference for Dirichlet process mixtures→Variational Algorithms for Approximate Bayesian InferenceLegacy edge — source detail unavailable
- Variational inference for Dirichlet process mixtures→A Constructive Definition of Dirichlet PriorsLegacy edge — source detail unavailable
- Variational inference for Dirichlet process mixtures→Gibbs Sampling Methods for Stick-Breaking PriorsLegacy edge — source detail unavailable
- Latent dirichlet allocation→An Introduction to Variational Methods for Graphical ModelsLegacy edge — source detail unavailable
- Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems→A Bayesian Analysis of Some Nonparametric ProblemsLegacy edge — source detail unavailable
- Gibbs Sampling Methods for Stick-Breaking Priors→Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric ProblemsLegacy edge — source detail unavailable
- Gibbs Sampling Methods for Stick-Breaking Priors→A Bayesian Analysis of Some Nonparametric ProblemsLegacy edge — source detail unavailable
- Gibbs Sampling Methods for Stick-Breaking Priors→Markov Chain Sampling Methods for Dirichlet Process Mixture ModelsLegacy edge — source detail unavailable
- Gibbs Sampling Methods for Stick-Breaking Priors→Bayesian Density Estimation and Inference Using MixturesLegacy edge — source detail unavailable
- Gibbs Sampling Methods for Stick-Breaking Priors→A Constructive Definition of Dirichlet PriorsLegacy edge — source detail unavailable
- Markov Chain Sampling Methods for Dirichlet Process Mixture Models→Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric ProblemsLegacy edge — source detail unavailable
- Markov Chain Sampling Methods for Dirichlet Process Mixture Models→A Bayesian Analysis of Some Nonparametric ProblemsLegacy edge — source detail unavailable
- Markov Chain Sampling Methods for Dirichlet Process Mixture Models→Bayesian Density Estimation and Inference Using MixturesLegacy edge — source detail unavailable
- Bayesian Density Estimation and Inference Using Mixtures→Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric ProblemsLegacy edge — source detail unavailable
- Bayesian Density Estimation and Inference Using Mixtures→A Bayesian Analysis of Some Nonparametric ProblemsLegacy edge — source detail unavailable
- Variational Algorithms for Approximate Bayesian Inference→An Introduction to Variational Methods for Graphical ModelsLegacy edge — source detail unavailable
- Variational Algorithms for Approximate Bayesian Inference→Markov Chain Sampling Methods for Dirichlet Process Mixture ModelsLegacy edge — source detail unavailable
- Graphical Models, Exponential Families, and Variational Inference→An Introduction to Variational Methods for Graphical ModelsLegacy edge — source detail unavailable
- Graphical Models, Exponential Families, and Variational Inference→Latent dirichlet allocationLegacy edge — source detail unavailable
- Graphical Models, Exponential Families, and Variational Inference→Variational Algorithms for Approximate Bayesian InferenceLegacy edge — source detail unavailable
- Stochastic variational inference→An Introduction to Variational Methods for Graphical ModelsLegacy edge — source detail unavailable
- Stochastic variational inference→Latent dirichlet allocationLegacy edge — source detail unavailable
- Stochastic variational inference→Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric ProblemsLegacy edge — source detail unavailable
- Stochastic variational inference→A Bayesian Analysis of Some Nonparametric ProblemsLegacy edge — source detail unavailable
- Stochastic variational inference→Markov Chain Sampling Methods for Dirichlet Process Mixture ModelsLegacy edge — source detail unavailable
- Stochastic variational inference→Bayesian Density Estimation and Inference Using MixturesLegacy edge — source detail unavailable
- Stochastic variational inference→Graphical Models, Exponential Families, and Variational InferenceLegacy edge — source detail unavailable
- Variational Inference: A Review for Statisticians→An Introduction to Variational Methods for Graphical ModelsLegacy edge — source detail unavailable
- Variational Inference: A Review for Statisticians→An Introduction to Variational Methods for Graphical ModelsLegacy edge — source detail unavailable
- Variational Inference: A Review for Statisticians→Latent dirichlet allocationLegacy edge — source detail unavailable
- Variational Inference: A Review for Statisticians→Graphical Models, Exponential Families, and Variational InferenceLegacy edge — source detail unavailable
- Variational Inference: A Review for Statisticians→Stochastic variational inferenceLegacy edge — source detail unavailable
What this paper cites, inside the corpus
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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