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Inference algorithms and learning theory for Bayesian sparse factor analysis


Stegle,  O
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Rattray, M., Stegle, O., Sharp, K., & Winn, J. (2009). Inference algorithms and learning theory for Bayesian sparse factor analysis. Journal of Physics: Conference Series, 197(1: International Workshop on Statistical-Mechanical Informatics 2009), 1-10. doi:10.1088/1742-6596/197/1/012002.

Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.