From Distance Correlation to Multiscale Graph Correlation

Cencheng Shen, Carey E. Priebe and Joshua T. Vogelstein

Journal of the American Statistical Association, 2020, vol. 115, issue 529, 280-291

Abstract: 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. Supplementary materials for this article are available online.

Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (9)

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2018.1543125 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:115:y:2020:i:529:p:280-291

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2018.1543125

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().