  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.
