From Distance Correlation to Multiscale Graph Correlation

• 成果类型: Article
• 署名作者: Shen, Cencheng; Priebe, Carey E.; Vogelstein, Joshua T.
• 署名单位: University of Delaware; Johns Hopkins University; Johns Hopkins University; Johns Hopkins University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1543125
• 发表日期: 2020
• 页码: 280-291
• 关键词: dimensionality reduction; local efficiency; INDEPENDENCE; dependence; statistics

摘要

Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we establish a new framework that generalizes distance correlation (Dcorr)-a correlation measure that was recently proposed and shown to be universally consistent for dependence testing against all joint distributions of finite moments-to the multiscale graph correlation (MGC). By using the characteristic functions and incorporating the nearest neighbor machinery, we formalize the population version of local distance correlations, define the optimal scale in a given dependency, and name the optimal local correlation as MGC. The new theoretical framework motivates a theoretically sound sample MGC and allows a number of desirable properties to be proved, including the universal consistency, convergence, and almost unbiasedness of the sample version. The advantages of MGC are illustrated via a comprehensive set of simulations with linear, nonlinear, univariate, multivariate, and noisy dependencies, where it loses almost no power in monotone dependencies while achieving better performance in general dependencies, compared to Dcorr and other popular methods. for this article are available online.