Distance-Based Independence Screening for Canonical Analysis

This paper introduces a novel method called Distance-Based Independence Screening for Canonical Analysis (DISCA) that performs simultaneous dimension reduction for a pair of random variables by optimizing the distance covariance (dCov). dCov is a statistic first proposed by Sz\'ekely et al. [2009] for independence testing. Compared with sufficient dimension reduction (SDR) and canonical correlation analysis (CCA)-based approaches, DISCA is a model-free approach that does not impose dimensional or distributional restrictions on variables and is more sensitive to nonlinear relationships. Theoretically, we establish a non-asymptotic error bound to provide a guarantee of our method's performance. Numerically, DISCA performs comparable to or better than other state-of-the-art algorithms and is computationally faster. All codes of our DISCA method can be found on GitHub https : //github.com/Yijin911/DISCA.git, including an R package named DISCA.