  Canonical Correlation Analysis (CCA) is a classical tool for finding
correlations among the components of two random vectors. In recent years, CCA
has been widely applied to the analysis of genomic data, where it is common for
researchers to perform multiple assays on a single set of patient samples.
Recent work has proposed sparse variants of CCA to address the high
dimensionality of such data. However, classical and sparse CCA are based on
linear models, and are thus limited in their ability to find general
correlations. In this paper, we present two approaches to high-dimensional
nonparametric CCA, building on recent developments in high-dimensional
nonparametric regression. We present estimation procedures for both approaches,
and analyze their theoretical properties in the high-dimensional setting. We
demonstrate the effectiveness of these procedures in discovering nonlinear
correlations via extensive simulations, as well as through experiments with
genomic data.
