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CATEGORIES:Information Theory Seminar
SUMMARY:The Role of Information Measures on the Regulariza
 tion of Empirical Risk Minimization - Dr Iñaki Esn
 aola\, University of Sheffield
DTSTART;TZID=Europe/London:20231129T140000
DTEND;TZID=Europe/London:20231129T150000
UID:TALK205339AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/205339
DESCRIPTION:The empirical risk minimization problem with relat
 ive entropy regularization (ERM-RER) is presented 
 considering that the reference measure is a $\\sig
 ma$-finite measure instead of a probability measur
 e. This generalization allows for a larger degree 
 of flexibility in the incorporation of prior knowl
 edge over the set of models. We discuss the interp
 lay of the regularization parameter\, the referenc
 e measure\, the risk measure\, and the expected em
 pirical risk induced by the solution of the ERM-RE
 R problem\, which is proved to be unique. We show 
 that the expectation of the sensitivity is upper b
 ounded\, up to a constant factor\, by the square r
 oot of the lautum information between the models a
 nd the datasets. Using these tools\, dataset aggre
 gation is studied and different figures of merit t
 o evaluate the generalization capabilities of ERM-
 RER are introduced. For arbitrary datasets and par
 ameters of the ERM-RER solution\, a connection bet
 ween Jeffrey’s divergence\, training\, and test er
 ror is established. We conclude by extending the r
 esults to $f$-divergence regularization by obtaini
 ng a closed form expression for the solution under
  mild assumptions on the structure of the regulari
 zer. This analytical solution is leveraged to char
 acterize the sensitivity of the resulting supervis
 ed learning problem and we evaluate the solution f
 or specific regularizers arising in estimation\, h
 igh-dimensional statistics\, and hypothesis testin
 g. \n\n
LOCATION:MR5\, CMS Pavilion A
CONTACT:Prof. Ramji Venkataramanan
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