## Infinite sparse factor analysis and infinite independent components analysis.(English)Zbl 1173.94367

Davies, Mike E. (ed.) et al., Independent component analysis and signal separation. 7th international conference, ICA 2007, London, UK, September 9–12, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-74493-1/pbk). Lecture Notes in Computer Science 4666, 381-388 (2007).
Summary: 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.
For the entire collection see [Zbl 1129.94002].

### MSC:

 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 62H25 Factor analysis and principal components; correspondence analysis
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