  Canonical correlation analysis (CCA) is a classical and important
multivariate technique for exploring the relationship between two sets of
continuous variables. CCA has applications in many fields, such as genomics and
neuroimaging. It can extract meaningful features as well as use these features
for subsequent analysis. Although some sparse CCA methods have been developed
to deal with high-dimensional problems, they are designed specifically for
continuous data and do not consider the integer-valued data from
next-generation sequencing platforms that exhibit very low counts for some
important features. We propose a model-based probabilistic approach for
correlation and canonical correlation estimation for two sparse count data sets
(PSCCA). PSCCA demonstrates that correlations and canonical correlations
estimated at the natural parameter level are more appropriate than traditional
estimation methods applied to the raw data. We demonstrate through simulation
studies that PSCCA outperforms other standard correlation approaches and sparse
CCA approaches in estimating the true correlations and canonical correlations
at the natural parameter level. We further apply the PSCCA method to study the
association of miRNA and mRNA expression data sets from a squamous cell lung
cancer study, finding that PSCCA can uncover a large number of strongly
correlated pairs than standard correlation and other sparse CCA approaches.
