Paper No: 56
Infinite Sparse Factor Analysis and Infinite Independent Components Analysis
Author(s): David Knowles, Zoubin Ghahramani
An extension of Independent Components Analysis (ICA) is proposed where observed data Yis modelled as a linear superposition, $\G$, of a potentially infinite number of hidden sources, X. Whether a given source is active for a specific data point is specified by an infinite binary matrix, Z, so Y=G(Z.*X)+E. We define a prior on Z using the Indian Buffet Process (IBP). We describe four variants of the model, with Gaussian or Laplacian priors on X and the one or two-parameter IBPs. We demonstrate inference under these models using a Markov Chain Monte Carlo (MCMC) algorithm on synthetic and gene expression data.