  Canonical correlation analysis investigates linear relationships between two
sets of variables, but often works poorly on modern data sets due to
high-dimensionality and mixed data types such as continuous, binary and
zero-inflated. To overcome these challenges, we propose a semiparametric
approach for sparse canonical correlation analysis based on Gaussian copula.
Our main contribution is a truncated latent Gaussian copula model for data with
excess zeros, which allows us to derive a rank-based estimator of the latent
correlation matrix for mixed variable types without the estimation of marginal
transformation functions. The resulting canonical correlation analysis method
works well in high-dimensional settings as demonstrated via numerical studies,
as well as in application to the analysis of association between gene
expression and micro RNA data of breast cancer patients.
