nference algorithms and learning theory for Bayesian sparse factor analysis
Magnus Rattray, Oliver Stegle, Kevin Sharp and John M. Winn
In: International Workshop on Statistical-Mechanical Informatics 2009(2209).
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.
|EPrint Type:||Conference or Workshop Item (Paper)|
|Project Keyword:||Project Keyword UNSPECIFIED|
|Subjects:||Theory & Algorithms|
|Deposited By:||Oliver Stegle|
|Deposited On:||08 March 2010|