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SUMMARY:Geometry-oriented Measures of Dependence
DTSTART;VALUE=DATE-TIME:20240222T111500
DTEND;VALUE=DATE-TIME:20240222T121500
DTSTAMP;VALUE=DATE-TIME:20240519T200351Z
UID:c95961a3ea6868ae1cf1bc9bac9bb3f26eddee7863ff514e2682955c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Anatoly Khina\nSchool of Electrical Engineering\nTel Avi
v University\nOne of the fundamental problems of statistics and data scien
ce is identifying and measuring dependence. This problem dates back to the
works of Bravais\, Galton\, and Pearson in the 18^th century on dependenc
e measure design\, and to the work of Rényi in the late 1950s on axiomati
zing the desired properties of such measures. For discrete random variable
s\, categorical dependence measures—primarily those based on Shannon's m
utual information and entropy\, and maximal correlation—are valid choice
s when only the information content is important.\n \nHowever\, when some
possible underlying physical interpretation is of the essence\, other mea
sures need to be sought after. Consequently\, much effort has been put int
o both the design and property axiomatization of such dependence measures
when the dependence strength is dictated by the inference quality with res
pect to some metric.\n \nIn this talk\, I will first propose a new set of
natural axioms that reflect desired innate geometric properties. I will s
how that\, in fact\, none of the existing dependence measures satisfies
this set of axioms and has a known feasible evaluation algorithm. Finally\
, I will propose a new computationally efficient dependence measure that s
atisfies all the proposed axioms and compare its performance to that of cl
assical dependence measures such as maximal correlation and correlation ra
tio\, as well as recently proposed measures such as xicor (Chatterjee JASA
‘21)\, distance correlation (Székely et al. Ann. Stat. ‘07)\, and ma
ximal information coefficient (Reshef et al. Science ‘11).\n \nJoint wo
rk with Elad Domanovitz and Yoad Nitzan.
LOCATION:BC 129 https://plan.epfl.ch/?room==BC%20129
STATUS:CONFIRMED
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