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SUMMARY:Geometrizing rates of convergence under local differential privacy
  - Lukas Steinberger\, University of Freiburg
DTSTART:20190607T150000Z
DTEND:20190607T160000Z
UID:TALK124021@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:One of the many new challenges for data analysis in the inform
 ation age is the increasing concern of privacy protection. A particularly 
 fruitful approach to data protection that has recently received a lot of a
 ttention\, is the notion of `local differential privacy’. The idea is th
 at each data providing individual releases only a randomly perturbed versi
 on of its original data\, where the randomization mechanism is required to
  satisfy a precise privacy definition. \n \nIn this talk\, we discuss the 
 impact of a local differential privacy guarantee on the quality of statist
 ical estimation. In this setup\, the objective is not only to come up with
  an optimal estimation procedure that efficiently recovers information fro
 m the privatized observations\, but also to devise a privatization mechani
 sm that best facilitates subsequent estimation while respecting the requir
 ed privacy provisions. In the general context of estimating linear functio
 nals of the unknown true data generating distribution\, we characterize th
 e minimax rate of private estimation in terms of a certain modulus of cont
 inuity of the functional to be estimated and provide a construction of min
 imax rate optimal privatization mechanisms. Somewhat surprisingly\, it can
  be shown that simple sample means of appropriately randomized observation
 s are always optimal for estimating linear functionals. Our analysis also 
 allows for a quantification of the price of local differential privacy in 
 terms of loss of statistical accuracy. This price appears to be highly pro
 blem dependent.
LOCATION:MR12
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