Plenary Lecture

Equitability and Dependence Measures

Professor Adam Ding
Department of Mathematics
567 Lake Hall
Northeastern University
Boston, USA

Abstract: Reshef et al. (Science, 2011) proposed the concept of equitability that dependence measures should satisfy: treating all types of functional relationships, linear and nonlinear, equally. Traditional measures such as Pearson’s correlation prefer linear relationship and are inadequate to learn the complex structures in large data set. A novel measure, the maximal information coefficient (MIC), is proposed in Reshef et al. (2011). Recently, Kinney and Atwal (Proceedings of the National Academy of Sciences of the United States of America, 2014) showed that MIC is in fact not equitable under a strict mathematical definition. They showed that the equitability is satisfied by a fundamental quantity in information theory, the mutual information (MI). We discuss the equitability and other theoretical properties of several state-of-art dependence measures including MI, MIC and distance correlation (dcor). The relationship between equitability and copula based dependence measures is clarified. The mathematical properties of a new dependence measure, the copula correlation (Ccor), are studied and compared with existing measures. Ccor is equitable, and reflects correctly the proportion of deterministic relationships hidden in stochastic noise.

Brief Biography of the Speaker: Adam Ding received his Ph.D. degree from Cornell University in 1996. Since then, he has been a faculty member with the Mathematics Department of Northeastern University. He had hold visiting faculty positions in Harvard University and University of Rochester. His research focus on statistical methodology and applications in biostatistics, engineering and finance.