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SUMMARY:Semiparametric privacy-constrained inference
DTSTART:20250707T090000Z
DTEND:20250707T100000Z
DTSTAMP:20260510T094200Z
UID:indico-event-14027@indico.math.cnrs.fr
DESCRIPTION:Speakers: Thibault Randrianarisoa (BIDSA\, Bocconi University)
 \n\nWe study the problem of non-parametric density estimation for densitie
 s in Sobolev spaces\, under the additional constraint that only privatized
  data are allowed to be published and available for inference. More precis
 ely\, we focus on the estimation of a functional of the density via plug-i
 n estimators. For this purpose\, we adapt recent results from the minimax 
 theory under the framework of local α-differential privacy. We first buil
 d a nonparametric projection estimator based on spline wavelets and add su
 itably scaled Laplace noise to empirical wavelet coefficients to fulfill t
 he privacy requirement. Under some regularity assumptions of the functiona
 l\, we derive convergence rates in expectation for the corresponding plug-
 in estimators and show that these are optimal up to a logarithmic factor. 
 We observe different regimes in the rate\, depending on the size of α and
  the regularity of the functional. We also provide a Lepski-type estimator
  that adapts to the Sobolev regularity of the density. \n\nhttps://indico
 .math.cnrs.fr/event/14027/
LOCATION:Amphi L. Schwartz (1R3\, RDC)
URL:https://indico.math.cnrs.fr/event/14027/
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