Table of Contents
What is Dirichlet process mixture model?
The Dirichlet process is a stochastic proces used in Bayesian nonparametric models of data, particularly in Dirichlet process mixture models (also known as infinite mixture models). It is a distribution over distributions, i.e. each draw from a Dirichlet process is itself a distribution.
What is Dirichlet regression?
Introduction. Dirichlet regression can be used to predict the ratio in which the sum total X (demand/forecast/estimate) can be distributed among the component Ys. It is practically a case where there are multiple dependent ‘Y’ variables and one predictor X variable, whose sum is distributed among the Ys .
What is Chinese restaurant algorithm?
In probability theory, the Chinese restaurant process is a discrete-time stochastic process, analogous to seating customers at tables in a Chinese restaurant. Imagine a Chinese restaurant with an infinite number of circular tables, each with infinite capacity. Customer 1 sits at the first table.
What is EM machine learning?
The Expectation-Maximization Algorithm, or EM algorithm for short, is an approach for maximum likelihood estimation in the presence of latent variables. A general technique for finding maximum likelihood estimators in latent variable models is the expectation-maximization (EM) algorithm.
What is EM in clustering?
EM is an iterative method which alternates between two steps, expectation (E) and maximization (M). For clustering, EM makes use of the finite Gaussian mixtures model and estimates a set of parameters iteratively until a desired convergence value is achieved. Iteratively refine the parameters with E and M steps.
What is the Dirichlet process in statistics?
Dirichlet process. In the same way as the Dirichlet distribution is the conjugate prior for the categorical distribution, the Dirichlet process is the conjugate prior for infinite, nonparametric discrete distributions. A particularly important application of Dirichlet processes is as a prior probability distribution in infinite mixture models .
What is dirdirichlet process?
Dirichlet processes are usually used when modelling data that tends to repeat previous values in a so-called “rich get richer” fashion.
What is the application of Dirichlet process in machine learning?
A particularly important application of Dirichlet processes is as a prior probability distribution in infinite mixture models . The Dirichlet process was formally introduced by Thomas Ferguson in 1973. It has since been applied in data mining and machine learning, among others for natural language processing, computer vision and bioinformatics .
Is the posterior distribution of the Dirichlet process conjugate?
The Dirichlet Process distribution satisfies prior conjugacy, posterior consistency, and the Bernstein–von Mises theorem. In this model, the posterior distribution is again a Dirichlet process. This means that the Dirichlet process is a conjugate prior for this model.