Machine Learning

, Volume 97, Issue 1–2, pp 103–127

A constrained matrix-variate Gaussian process for transposable data

Article

DOI: 10.1007/s10994-014-5444-1

Cite this article as:
Koyejo, O., Lee, C. & Ghosh, J. Mach Learn (2014) 97: 103. doi:10.1007/s10994-014-5444-1

Abstract

Transposable data represents interactions among two sets of entities, and are typically represented as a matrix containing the known interaction values. Additional side information may consist of feature vectors specific to entities corresponding to the rows and/or columns of such a matrix. Further information may also be available in the form of interactions or hierarchies among entities along the same mode (axis). We propose a novel approach for modeling transposable data with missing interactions given additional side information. The interactions are modeled as noisy observations from a latent noise free matrix generated from a matrix-variate Gaussian process. The construction of row and column covariances using side information provides a flexible mechanism for specifying a-priori knowledge of the row and column correlations in the data. Further, the use of such a prior combined with the side information enables predictions for new rows and columns not observed in the training data. In this work, we combine the matrix-variate Gaussian process model with low rank constraints. The constrained Gaussian process approach is applied to the prediction of hidden associations between genes and diseases using a small set of observed associations as well as prior covariances induced by gene-gene interaction networks and disease ontologies. The proposed approach is also applied to recommender systems data which involves predicting the item ratings of users using known associations as well as prior covariances induced by social networks. We present experimental results that highlight the performance of constrained matrix-variate Gaussian process as compared to state of the art approaches in each domain.

Keywords

Constrained Bayesian inference Gaussian process Transposable data Nuclear norm Low rank 

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Imaging Research CenterUniversity of Texas at AustinAustinUSA
  2. 2.Department of Biomedical EngineeringUniversity of Texas at AustinAustinUSA
  3. 3.Department of Electrical and Computer EngineeringUniversity of Texas at AustinAustinUSA

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