Correlation

Physics

Mathematics

Latent variable

Parametric statistics

Statistics

Curse of dimensionality

Gaussian

Copula (linguistics)

Econometrics

Estimator

Canonical correlation

Semiparametric regression

Geometry

Quantum mechanics

Applied mathematics

Semiparametric model

Biometrika

Canonical correlation analysis investigates linear relationships between two sets of variables, but often works poorly on modern datasets due to high-dimensionality and mixed data types (continuous/binary/zero-inflated). We propose a new approach for sparse canonical correlation analysis of mixed data types that does not require explicit parametric assumptions. Our main contribution is the use of truncated latent Gaussian copula to model the data with excess zeroes, which allows us to derive a rank-based estimator of latent correlation matrix without the estimation of marginal transformation functions. The resulting semiparametric sparse canonical correlation analysis method works well in high-dimensional settings as demonstrated via numerical studies, and application to the analysis of association between gene expression and micro RNA data of breast cancer patients.

Sparse semiparametric canonical correlation analysis for data of mixed types