Plenary Lecture

Equitability and Dependence Measures

Professor Adam Ding
Department of Mathematics
Northeastern University
Boston, MA

Abstract: Reshef et al. (Science, 2011) proposed the concept of equitability that measures of dependence should satisfy: treating all types of functional relationships, linear and nonlinear, equally. To this end, they proposed a novel measure, the maximal information coefficient (MIC). Recently, Kinney and Atwal (2014) showed that MIC is in fact not equitable under a strict mathematical definition, while recommending the self-equitable mutual information (MI). We propose a new equitability definition to select among the many self-equitable measures. The copula correlation (Ccor), based on the $L_1$-distance of copula density, is shown to be equitable under all equitability definitions. We also prove theoretically that Ccor is much easier to estimate than MI. Simulations and real data analyses are used to illustrate advantage of equitable measures in feature selection.

Brief Biography of the Speaker: Adam Ding received his Ph.D. degree from Cornell University and has been a faculty member with the Mathematics Department of Northeastern University afterwards. He previously hold visiting faculty positions in Harvard University and University of Rochester. He has conducted research on statistical methodology and applications in biostatistics, engineering and finance. He has published numerous papers in Journal of American Statistical Association, Journal of the Royal Statistical Society Series B, Biostatistics, Biometrics, Biometrika, etc. His current research focus includes nonlinear dependence measures, cybersecurity, survival analysis.