Bayesian Statistics: Indian Buffet Process

A common goal of unsupervised learning is to discover the latent variables responsible for generating the observed properties of a set of objects. For example, factor analysis attempts to find a set of latent variables (or factors) that explain the correlations among the observed variables. A problem with factor analysis, however, is that the user has to specify the number of latent variables when using this technique. Should one use 5, 10, or 15 latent variables (or some other number)? There are at least two ways one can address this question. One way is by performing model selection. Another way is to use a Bayesian nonparametric method. In general, Bayesian nonparametric methods grow the number of parameters as the size and complexity of the data set grow. An important example of a Bayesian nonparametric method is the Indian Buffet Process. (Another important example is the Dirichlet Process Mixture Model; see the Computational Cognition Cheat Sheet on Dirichlet Processes.)