Bayesian Analysis

Beta Processes, Stick-Breaking and Power Laws

Tamara Broderick, Michael I. Jordan, and Jim Pitman

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The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binary-valued features. Recent work has provided stick-breaking representations for the beta process analogous to the well-known stick-breaking representation for the Dirichlet process. We derive one such stick-breaking representation directly from the characterization of the beta process as a completely random measure. This approach motivates a three-parameter generalization of the beta process, and we study the power laws that can be obtained from this generalized beta process. We present a posterior inference algorithm for the beta-Bernoulli process that exploits the stick-breaking representation, and we present experimental results for a discrete factor-analysis model.

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Bayesian Anal., Volume 7, Number 2 (2012), 439-476.

First available in Project Euclid: 16 June 2012

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beta process stick-breaking power law


Broderick, Tamara; Jordan, Michael I.; Pitman, Jim. Beta Processes, Stick-Breaking and Power Laws. Bayesian Anal. 7 (2012), no. 2, 439--476. doi:10.1214/12-BA715.

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