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 de-
rive 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
representa
%0 Journal Article
%1 broderick2012processes
%A Broderick, Tamara
%A Jordan, Michael I.
%A Pitman, Jim
%D 2012
%I Institute of Mathematical Statistics
%J Bayesian Anal.
%K Dirichlet_process beta-binomial beta_process machine_learning stick_breaking
%N 2
%P 439--476
%R 10.1214/12-ba715
%T Beta Processes, Stick-Breaking and Power Laws
%U http://dx.doi.org/10.1214/12-BA715
%V 7
%X 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 de-
rive 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
representa
@article{broderick2012processes,
abstract = {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 de-
rive 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
representa},
added-at = {2016-06-27T22:06:43.000+0200},
author = {Broderick, Tamara and Jordan, Michael I. and Pitman, Jim},
biburl = {https://www.bibsonomy.org/bibtex/2e5bde0a552a4bc2ead877167d441e3be/peter.ralph},
doi = {10.1214/12-ba715},
interhash = {35125129b03e64b0e7b74c4d9de1f3b0},
intrahash = {e5bde0a552a4bc2ead877167d441e3be},
journal = {Bayesian Anal.},
keywords = {Dirichlet_process beta-binomial beta_process machine_learning stick_breaking},
month = jun,
number = 2,
pages = {439--476},
publisher = {Institute of Mathematical Statistics},
timestamp = {2016-06-27T22:06:43.000+0200},
title = {Beta Processes, Stick-Breaking and Power Laws},
url = {http://dx.doi.org/10.1214/12-BA715},
volume = 7,
year = 2012
}