Infinite Sparse Factor Analysis and Infinite Independent Components Analysis
David Knowles and Zoubin Ghahramani
In: 7th International Conference on Independent Component Analysis and Signal Separation, London(2007).

Abstract

A nonparametric Bayesian extension of Independent Com- ponents Analysis (ICA) is proposed where observed data Y is 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. The resulting sparse rep- resentation allows increased data reduction compared to standard ICA. We define a prior on Z using the Indian Buffet Process (IBP). We de- scribe four variants of the model, with Gaussian or Laplacian priors on X and the one or two-parameter IBPs. We demonstrate Bayesian inference under these models using a Markov Chain Monte Carlo (MCMC) algo- rithm on synthetic and gene expression data and compare to standard ICA algorithms.

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