Dirichlet process

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Overview

Probability theory Peter Gustav Lejeune Dirichlet Stochastic processes Realizations Probability distributions

27 related topics

Applications of the Dirichlet process

Unsupervised learning Simplex Sign test Wilcoxon rank-sum test Wilcoxon signed-rank test

6 related topics

Alternative views

Chinese restaurant process Stick-breaking process Indicator function Beta distribution Pólya urn scheme

6 related topics

Use in Dirichlet mixture models

Data clustering Bernoulli random variable K-means Variance Gibbs sampler

6 related topics

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Alternative views

Use as a prior distribution

Use in Dirichlet mixture models

Data clustering
Bernoulli random variable Bernoulli distribution
K-means K-means clustering
Variance
Gibbs sampler
Inference Statistical inference

Applications of the Dirichlet process

Related distributions

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Map overview Semantic statistics

Nodes73

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Triples112

Avg. degree1.97

Density0.027397

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Dirichlet process

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related to External links · 21

Dirichlet process → All ThatPeter Green's, Bayesian, Chinese Restaurant Processes, Clustering, Dirichlet, Dirichlet Distribution, Dirichlet Processes, Dirichlet ProcessesPeter Green's, Example, Frigyik, Ghahramani's UAI, GuptaYee Whye Teh's, Infinite Mixture ModelsA Toy, Introduction, Jordan's NIPS, Kapila, NIPS, Nonparametric Bayesian, Nonparametric Bayesian Methods, Related Processes

related to The Pólya urn scheme · 11

Dirichlet process → Blackwell, Chinese, Dirichlet, Each, If, Imagine, MacQueen, Otherwise, Pólya, Then, Yet

has application · 10

Dirichlet process → Additionally, As, Bayesian, Dirichlet, For, Gaussian, Gaussians, In, Nonparametric, The

related to Bernstein–Von Mises theorem · 7

Dirichlet process → Bernstein, Brownian Bridge, Dirichlet, Donsker, In, Mises, Suppose

related to The Chinese restaurant process · 7

Dirichlet process → Additionally, After, Chinese, Dirichlet, Imagine, The, This

related to The stick-breaking process · 7

Dirichlet process → As, Beta, Conceptually, Dirichlet, In, Remember, Since

related to Alternative views · 6

Dirichlet process → Besides, Beta, Chinese, Dirichlet, Finetti's, There

related to Example 2 · 6

Dirichlet process → As, By, Denoting, Dirichlet, In, We

related to Formal definition · 5

Dirichlet process → Dir, Dirichlet, DP, For, Given

is a · 4

Dirichlet process → conjugate prior for infinite, conjugate prior for this model, probability distribution whose range is itself a set of probability distributions, so-called stick-breaking process view

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Important terminology

distribution dirichlet displaystyle process probability distributions model prior random alpha data number clusters infinite cluster discrete nonparametric used base posterior

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Dirichlet process	is a	probability distribution whose range is itself a set of probability distributions	0.90	text
Dirichlet process	is a	conjugate prior for infinite	0.90	text
Dirichlet process	is a	so-called stick-breaking process view	0.90	text
Dirichlet process	is a	conjugate prior for this model	0.90	text
k-means	instance of	By looking at how votes were cast in previous years on similar pieces of legislation one could fit a predictive model using a simple clustering algorithm	0.80	text
a religion	instance of	attributes	0.80	text
class or race could also be critical for modelling voter behaviour	instance of	attributes	0.80	text
resulting in more clusters in the model.Example 2As another example	instance of	attributes	0.80	text
we might be interested in modelling the velocities of galaxies using a simple model assuming that the velocities are clustered	instance of	attributes	0.80	text
for instance by assuming each velocity is distributed according to the normal distribution v i	instance of	attributes	0.80	text
resulting in more clusters in the model	instance of	attributes	0.80	text
Dirichlet process	has application	Dirichlet	0.60	section

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Explore this topic

Overview

Applications of the Dirichlet process

Alternative views

Use in Dirichlet mixture models

Key facts & relationships

Topics to explore

Overview

Introduction

Formal definition

Alternative views

Use as a prior distribution

Use in Dirichlet mixture models

Applications of the Dirichlet process

Related distributions

Advanced semantic analysis

Map overview Semantic statistics

Dirichlet process

How this topic connects Entity context

Dirichlet process

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges