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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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