Bayesian Group Factor Analysis

We introduce a factor analysis model that summarizes the dependencies between observed variable groups, instead of dependencies between individual variables as standard factor analysis does. A group may correspond to one view of the same set of objects, one of many data sets tied by co-occurrence, or a set of alternative variables collected from statistics tables to measure one property of interest. We show that by assuming groupwise sparse factors, active in a subset of the sets, the variation can be decomposed into factors explaining relationships between the sets and factors explaining away set-specific variation. We formulate the assumptions in a Bayesian model providing the factors, and apply the model to two data analysis tasks, in neuroimaging and chemical systems biology.

[1]  Samuel Kaski,et al.  Bayesian CCA via Group Sparsity , 2011, ICML.

[2]  M. Hulle,et al.  Functional connectivity analysis of fMRI data based on regularized multiset canonical correlation analysis , 2011, Journal of Neuroscience Methods.

[3]  A. Tenenhaus,et al.  Regularized Generalized Canonical Correlation Analysis , 2011, Eur. J. Oper. Res..

[4]  Zoubin Ghahramani,et al.  Nonparametric Bayesian Sparse Factor Models with application to Gene Expression modelling , 2010, The Annals of Applied Statistics.

[5]  Polina Golland,et al.  Categories and Functional Units: An Infinite Hierarchical Model for Brain Activations , 2010, NIPS.

[6]  Trevor Darrell,et al.  Factorized Latent Spaces with Structured Sparsity , 2010, NIPS.

[7]  Ali Jalali,et al.  A Dirty Model for Multi-task Learning , 2010, NIPS.

[8]  Hartwig R. Siebner,et al.  Infinite Relational Modeling of Functional Connectivity in Resting State fMRI , 2010, NIPS.

[9]  Ning Chen,et al.  Predictive Subspace Learning for Multi-view Data: a Large Margin Approach , 2010, NIPS.

[10]  Jean-Baptiste Poline,et al.  A group model for stable multi-subject ICA on fMRI datasets , 2010, NeuroImage.

[11]  Alexander Ilin,et al.  Transformations in variational Bayesian factor analysis to speed up learning , 2010, Neurocomputing.

[12]  Francis R. Bach,et al.  Structured Sparse Principal Component Analysis , 2009, AISTATS.

[13]  Lawrence Carin,et al.  Nonparametric factor analysis with beta process priors , 2009, ICML '09.

[14]  Francis R. Bach,et al.  Sparse probabilistic projections , 2008, NIPS.

[15]  Hal Daumé,et al.  The Infinite Hierarchical Factor Regression Model , 2008, NIPS.

[16]  Zoubin Ghahramani,et al.  Infinite Sparse Factor Analysis and Infinite Independent Components Analysis , 2007, ICA.

[17]  Mohamed Hanafi,et al.  Analysis of K sets of data, with differential emphasis on agreement between and within sets , 2006, Comput. Stat. Data Anal..

[18]  Paul A Clemons,et al.  The Connectivity Map: Using Gene-Expression Signatures to Connect Small Molecules, Genes, and Disease , 2006, Science.

[19]  Curzio Rüegg,et al.  Non steroidal anti‐inflammatory drugs and COX‐2 inhibitors as anti‐cancer therapeutics: hypes, hopes and reality , 2003, Annals of medicine.