beta process
(45 minutes to learn)
Summary
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.
Context
This concept has the prerequisites:
- Dirichlet process (The Dirichlet process is a useful analogy for understanding the beta process.)
- Indian buffet process (The IBP is the sequential process for sampling from a Bernoulli process with a beta process base-measure.)
Core resources (read/watch one of the following)
-Free-
→ Levy Processes and Applications to Machine Learning (2008)
Supplemental resources (the following are optional, but you may find them useful)
-Free-
→ Hierarchical Models, Nested Models and Completely Random Measures (2010)
→ Nonparametric Bayesian Models (2009)
See also
- The IBP is often used in probabilistic models with binary latent features .