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How is the Dirichlet process mixture model used?
The Dirichlet process mixture model (Antoniak, 1974) adds a level to the hierar- chy, treating \as the parameter of the distribution of the nth observation. Given the discreteness of G, the DP mixture has an interpretation as a mixture model with an unbounded number of mixture components.
Which is Monte Carlo sampling method for Dirichlet mixtures?
Abstract Dirichlet process (DP) mixture models are the cornerstone of nonpara- metric Bayesian statistics, and the development of Monte-Carlo Markov chain (MCMC) sampling methods for DP mixtures has enabled their applications to a variety of practical data analysis problems.
How to derive posterior inference from a Dirichlet process Gaussian mixture?
In this post, I’ll explore implementing posterior inference for Dirichlet process Gaussian mixture models (GMMs) via the stick-breaking construction in various probabilistic programming languages.
Can a mixture model be used for efficient posterior inference?
It is true that for a particular class of DP mixture models (for carefully chosen priors), efficient posterior inference is just a matter of iterative and direct sampling from full conditionals. But this convenience is not available in general, and we still have the issue of varying number of mixture components.
Which is an example of variational inference in parametric models?
For example, variational methods have been developed for parametric hierarchical Bayesian models based on general expo- nential family speci\\fcations (Ghahramani and Beal, 2001). MCMC methods have seen much wider application.
How are variational inference methods similar to MCMC?
Onesuchclassofalternativesisprovidedbyvariationalinferencemethods (Ghahra- mani and Beal, 2001; Jordan et al., 1999; Opper and Saad, 2001; Wainwright and Jordan, 2003; Wiegerinck, 2000). Like MCMC, variational inference methods have their roots in statistical physics, and, in contradistinction to MCMC methods, they are deterministic.
Can you restrict the number of components in a mixture model?
Abstract In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components.
Where did the idea of variational inference come from?
Like MCMC, variational inference methods have their roots in statistical physics, and, in contradistinction to MCMC methods, they are deterministic. The basic idea of variational inference is to formulate the compu- tation of a marginal or conditional probability in terms of an optimization problem.