the Indian Buffet Process: An Introduction and Review: Difference between revisions
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==Introduction== | ==Introduction== | ||
IBP is often used in factor analysis as a prior of infinite factors. | IBP is often used in factor analysis as a prior of infinite factors. | ||
IBP can be viewed as an extension of DP, where we drop the constraint <math> \sum_{i=1}^{\inf}{\pi_i}=1 </math> . | IBP can be viewed as an extension of DP, where we drop the constraint <math> \sum_{i=1}^{\inf}{\pi_i}=1 </math>. | ||
Because we drop the constraint, it does not naturally use IBP as a prior of mixture models. | |||
==Representations== | ==Representations== | ||
Like DP, IBP has several representations. | |||
===the limiting of finite distribution on sparse binary feature matrices=== | ===the limiting of finite distribution on sparse binary feature matrices=== | ||
We have N data points and K features and the possession of feature k by data point i is indicated by a binary variable <math> z_{ik} </math> | |||
The generative process of the binary feature matrix is defined as below: | |||
===stick breaking construction=== | |||
===the Indian buffet metaphor=== | ===the Indian buffet metaphor=== | ||
Revision as of 20:23, 9 August 2013
The Indian Buffet Process (IBP) is one of Bayesian nonparametric models, which is a prior measure on an infinite binary matrix. Unlike the Dirichlet process(DP), where each atom has negative correlation, IBP assumes each atom is independent.
Introduction
IBP is often used in factor analysis as a prior of infinite factors. IBP can be viewed as an extension of DP, where we drop the constraint [math]\displaystyle{ \sum_{i=1}^{\inf}{\pi_i}=1 }[/math]. Because we drop the constraint, it does not naturally use IBP as a prior of mixture models.
Representations
Like DP, IBP has several representations.
the limiting of finite distribution on sparse binary feature matrices
We have N data points and K features and the possession of feature k by data point i is indicated by a binary variable [math]\displaystyle{ z_{ik} }[/math] The generative process of the binary feature matrix is defined as below: