Publication

Dynamical Dirichlet Mixture Model

2007
Reports

Abstract

In this report, we propose a statistical model to deal with the discrete-distribution data varying over time. The proposed model -- HMM+DM -- extends the Dirichlet mixture model to the dynamic case: Hidden Markov Model with Dirichlet mixture output. Both the inference and parameter estimation procedures are proposed. Experiments on the generated data verify the proposed algorithms. Finally, we discuss the potential applications of the current model.

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2007
Reports

Abstract

Official source

Related concepts (32)

Dirichlet-multinomial distribution

In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector , and an observation drawn from a multinomial distribution with probability vector p and number of trials n.

Dirichlet distribution

In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted , is a family of continuous multivariate probability distributions parameterized by a vector of positive reals. It is a multivariate generalization of the beta distribution, hence its alternative name of multivariate beta distribution (MBD). Dirichlet distributions are commonly used as prior distributions in Bayesian statistics, and in fact, the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution.

Mixture model

In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population.

Related publications (11)

Dynamical Dirichlet Mixture Model

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