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.

翻译：本文提出一种名为“基于距离的典型分析独立筛选”（DISCA）的新方法，该方法通过优化距离协方差（dCov）实现一对随机变量的同步降维。dCov是Székely等人[2009]首次提出的用于独立性检验的统计量。与基于充分降维（SDR）和典型相关分析（CCA）的方法相比，DISCA是一种无模型方法，不对变量施加维度或分布限制，且对非线性关系更为敏感。在理论上，我们建立了非渐近误差界以保障方法性能。在数值实验中，DISCA的性能与其他先进算法相当或更优，且计算速度更快。本文DISCA方法的所有代码（包括名为DISCA的R包）均可从GitHub https://github.com/Yijin911/DISCA.git 获取。