Infinite Latent Feature Models and the Indian Buffet Process
Thomas Griffiths and Zoubin Ghahramani
Gatsby Unit, London, UK.
We define a probability distribution over equivalence classes of binary matrices with a finite number of rows and an unbounded number of columns. This distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features. We derive the distribution by taking the limit of a distribution over N × K binary matrices as K goes to infinity, a strategy inspired by the derivation of the Chinese restaurant process (Aldous, 1985; Pitman, 2002) as the limit of a Dirichlet-multinomial model. This strategy preserves the exchangeability of the rows of matrices. We define several simple generative processes that result in the same distribution over equivalence classes of binary matrices, one of which we call the Indian buffet process. We illustrate the use of this distribution as a prior in an infinite latent feature model, deriving a Markov chain Monte Carlo algorithm for inference in this model and applying this algorithm to an artificial dataset.