Geometry-oriented Measures of Dependence in Statistical Analysis

Explore a one-hour lecture on geometry-oriented measures of dependence in statistics and data science, delivered by Professor Anatoly Khina from Tel Aviv University. Delve into the historical evolution of dependence measures from Bravais, Galton, and Pearson's early work through Rényi's axiomatization in the 1950s. Learn about the limitations of traditional categorical dependence measures based on Shannon's mutual information and maximal correlation when physical interpretations are crucial. Discover a new set of natural axioms reflecting geometric properties, understand why existing measures fall short, and examine a novel computationally efficient dependence measure that satisfies these axioms. Compare this new approach with classical methods like maximal correlation and correlation ratio, as well as modern measures including xicor, distance correlation, and maximal information coefficient. The lecture presents collaborative research conducted with Elad Domanovitz and Yoad Nitzan, drawing from Professor Khina's extensive background in Information Theory, Control Theory, Signal Processing, and Statistics.