  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.
