beta process

(45 minutes to learn)


The beta process is a random discrete measure that is completely described by a countably infinite set of atoms, where each atom has a finite mass determined from a stick-breaking process. Unlike the Dirichlet process, the weights of the atoms do not have to sum to one, but the masses must be between [0,1], and the marginals of the beta process are not beta distributed. The beta process can be used as a base measure for a Bernoulli process, i.e. to yield a stochastic process for binary random variables.


This concept has the prerequisites:

Core resources (read/watch one of the following)


Levy Processes and Applications to Machine Learning (2008)
Video lecture
Location: 12:10 - 33:00
Author: Romain Thibaux

Supplemental resources (the following are optional, but you may find them useful)


Hierarchical Models, Nested Models and Completely Random Measures (2010)
Location: Sections 2-3
Author: Michael I. Jordan
Nonparametric Bayesian Models (2009)
Location: part 2 from 50:00 onwards
Author: Yee Whye Teh

See also