An Introduction to Variational Methods for Graphical Models
Machine Learning
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Hierarchical kernel stick-breaking process for multi-task image analysis
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Multi-task compressive sensing with Dirichlet process priors
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The dynamic hierarchical Dirichlet process
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Variational bayesian dirichlet-multinomial allocation for exponential family mixtures
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Smooth image segmentation by nonparametric bayesian inference
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A spatially-constrained normalized Gamma process prior
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International Journal of Computer Vision
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Variational inference methods, including mean field methods and loopy belief propagation, have been widely used for approximate probabilistic inference in graphical models. While often less accurate than MCMC, variational methods provide a fast deterministic approximation to marginal and conditional probabilities. Such approximations can be particularly useful in high dimensional problems where sampling methods are too slow to be effective. A limitation of current methods, however, is that they are restricted to parametric probabilistic models. MCMC does not have such a limitation; indeed, MCMC samplers have been developed for the Dirichlet process (DP), a nonparametric distribution on distributions (Ferguson, 1973) that is the cornerstone of Bayesian nonparametric statistics (Escobar & West, 1995; Neal, 2000). In this paper, we develop a mean-field variational approach to approximate inference for the Dirichlet process, where the approximate posterior is based on the truncated stick-breaking construction (Ishwaran & James, 2001). We compare our approach to DP samplers for Gaussian DP mixture models.