Infinite Sparse Factor Analysis and Infinite Independent Components Analysis. Knowles, D. A. & Ghahramani, Z. In 7th International Conference on Independent Component Analysis and Signal Separation (ICA), 2007.
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A nonparametric Bayesian extension of Independent Components 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 representation allows increased data reduction compared to standard ICA. 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 Bayesian inference under these models using a Markov Chain Monte Carlo (MCMC) algorithm on synthetic and gene expression data and compare to standard ICA algorithms.

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