Tata Institute of Fundamental Research

Hilbert Schmidt Independence Criterion (HSIC)

STCS Student Seminar
Speaker: Jatin Batra
Organiser: Eeshan Modak
Date: Friday, 13 May 2022, 16:00 to 17:00
Venue: A-201 (STCS Seminar Room)

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Abstract:  Suppose we have access to n empirical observations of two random variables X,Y and we want to know - are X,Y independent? One way to answer this is to compute empirical versions of various statistical quantities like covariance and mutual information. However, because all we have access to is a finite number (n) of empirical observations, we might simply get unlucky. Can we guarantee that our test accuracy increases rapidly with n? The Hilbert Schmidt Independence Criterion (HSIC) proposed by Gretton, Bousquet, Smola and Scholkopft resolves this issue by providing an estimate of dependence that provably gets more accurate at a 1/n rate. In this talk, I will describe (following Gretton et al. in http://www.gatsby.ucl.ac.uk/~gretton/papers/GreBouSmoSch05.pdf) how HSIC arises quite naturally as a kernel invariant version of the covariance estimate and also allude to some later applications of HSIC.