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For instance, mixtures of Gaussian process experts, where the number of required experts must be inferred from the data. [8] [9] As draws from a Dirichlet process are discrete, an important use is as a prior probability in infinite mixture models. In this case, is the parametric set of component distributions. The generative process is ...
Very Fast and clean C implementation of the Expectation Maximization (EM) algorithm for estimating Gaussian Mixture Models (GMMs). mclust is an R package for mixture modeling. dpgmm Pure Python Dirichlet process Gaussian mixture model implementation (variational).
Dirichlet distributions are most commonly used as the prior distribution of categorical variables or multinomial variables in Bayesian mixture models and other hierarchical Bayesian models. (In many fields, such as in natural language processing , categorical variables are often imprecisely called "multinomial variables".
Gaussian processes can also be used in the context of mixture of experts models, for example. [28] [29] The underlying rationale of such a learning framework consists in the assumption that a given mapping cannot be well captured by a single Gaussian process model. Instead, the observation space is divided into subsets, each of which is ...
Bayesian inference is also often used for inference about finite mixture models. [2] The Bayesian approach also allows for the case where the number of components, , is infinite, using a Dirichlet process prior, yielding a Dirichlet process mixture model for clustering. [3]
As proposed in the original paper, [3] a sparse Dirichlet prior can be used to model the topic-word distribution, following the intuition that the probability distribution over words in a topic is skewed, so that only a small set of words have high probability. The resulting model is the most widely applied variant of LDA today.
The HDP mixture model is a natural nonparametric generalization of Latent Dirichlet allocation, where the number of topics can be unbounded and learnt from data. [1] Here each group is a document consisting of a bag of words, each cluster is a topic, and each document is a mixture of topics.
Types of generative models are: Gaussian mixture model (and other types of mixture model) Hidden Markov model; Probabilistic context-free grammar; Bayesian network (e.g. Naive bayes, Autoregressive model) Averaged one-dependence estimators; Latent Dirichlet allocation; Boltzmann machine (e.g. Restricted Boltzmann machine, Deep belief network)