Article

Machine Learning

, Volume 79, Issue 1, pp 201-226

Infinite factorization of multiple non-parametric views

  • Simon RogersAffiliated withDepartment of Computing Science, University of Glasgow
  • , Arto KlamiAffiliated withDepartment of Information and Computer Science, Helsinki University of Technology Email author 
  • , Janne SinkkonenAffiliated withDepartment of Information and Computer Science, Helsinki University of Technology
  • , Mark GirolamiAffiliated withDepartment of Computing Science, University of Glasgow
  • , Samuel KaskiAffiliated withDepartment of Information and Computer Science, Helsinki University of Technology

Abstract

Combined analysis of multiple data sources has increasing application interest, in particular for distinguishing shared and source-specific aspects. We extend this rationale to the generative and non-parametric clustering setting by introducing a novel non-parametric hierarchical mixture model. The lower level of the model describes each source with a flexible non-parametric mixture, and the top level combines these to describe commonalities of the sources. The lower-level clusters arise from hierarchical Dirichlet Processes, inducing an infinite-dimensional contingency table between the sources. The commonalities between the sources are modeled by an infinite component model of the contingency table, interpretable as non-negative factorization of infinite matrices, or as a prior for infinite contingency tables. With Gaussian mixture components plugged in for continuous measurements, the model is applied to two views of genes, mRNA expression and abundance of the produced proteins, to expose groups of genes that are co-regulated in either or both of the views. We discover complex relationships between the marginals (that are multimodal in both marginals) that would remain undetected by simpler models. Cluster analysis of co-expression is a standard method of screening for co-regulation, and the two-view analysis extends the approach to distinguishing between pre- and post-translational regulation.

Keywords

Hierarchical Dirichlet process Multi-view learning Contingency table Protein regulation