Geometry Oriented Measures Of Dependence

Electrical Engineering Systems Seminar

Speaker: Yoad Nitzan

M.Sc. student under the supervision of Dr. Anatoly Khina

Wednesday, 15^th May 2024, at 15:00

Room 011, Kitot Building, Faculty of Engineering

Geometry Oriented Measures Of Dependence

Abstract

One of the fundamental problems of statistics and data science is identifying dependence and measuring its strength. This problem dates to the works of Bravais, Galton, and Pearson in the 18th century on dependence measure design, and to the work of Rényi in the late 1950s on axiomatizing the desired properties of such measures. For discrete random variables, categorical dependence measures—primarily those based on Shannon’s mutual information and entropy, and maximal correlation—are valid choices when only the information content is important. However, when some possible underlying physical interpretation is of the essence, other measures need to be sought after. Consequently, significant effort has been put into both design and property axiomatization of dependence measures when the dependence strength is dictated by the inference quality with respect to some metric. We propose a new set of natural axioms that reflect desired innate geometric properties. We show that, in fact, none of the existing dependence measures satisfies this set of axioms and has a known feasible evaluation algorithm. Finally, we propose a new computationally efficient dependence measure that satisfies all the proposed axioms and compare its performance to that of existing dependence measures.

השתתפות בסמינר תיתן קרדיט שמיעה = עפ"י רישום שם מלא + מספר ת.ז. בדף הנוכחות שיועבר באולם במהלך הסמינר