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. Paper Pdf doi abstract bibtex 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.

@inproceedings{Knowles07iica,
Abstract = {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.},
Author = {Knowles, David A. and Ghahramani, Zoubin},
Booktitle = {7th International Conference on Independent Component Analysis and Signal Separation (ICA)},
Doi = {10.1007/978-3-540-74494-8},
Isbn = {978-3-540-74493-1},
Keywords = {Machine Learning/Statistics},
Title = {{Infinite Sparse Factor Analysis and Infinite Independent Components Analysis}},
Url = {http://www.springerlink.com/index/10.1007/978-3-540-74494-8},
Url_Pdf = {http://mlg.eng.cam.ac.uk/pub/pdf/KnoGha07.pdf},
Year = {2007}}

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