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CATEGORIES:Statistics
SUMMARY:Geometrizing rates of convergence under local diff
erential privacy - Lukas Steinberger\, University
of Freiburg
DTSTART;TZID=Europe/London:20190607T160000
DTEND;TZID=Europe/London:20190607T170000
UID:TALK124021AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/124021
DESCRIPTION:One of the many new challenges for data analysis i
n the information age is the increasing concern of
privacy protection. A particularly fruitful appro
ach to data protection that has recently received
a lot of attention\, is the notion of `local diffe
rential privacyâ€™. The idea is that each data provi
ding individual releases only a randomly perturbed
version of its original data\, where the randomiz
ation mechanism is required to satisfy a precise p
rivacy definition. \n \nIn this talk\, we discuss
the impact of a local differential privacy guarant
ee on the quality of statistical estimation. In th
is setup\, the objective is not only to come up wi
th an optimal estimation procedure that efficientl
y recovers information from the privatized observa
tions\, but also to devise a privatization mechani
sm that best facilitates subsequent estimation whi
le respecting the required privacy provisions. In
the general context of estimating linear functiona
ls of the unknown true data generating distributio
n\, we characterize the minimax rate of private es
timation in terms of a certain modulus of continui
ty of the functional to be estimated and provide a
construction of minimax rate optimal privatizatio
n mechanisms. Somewhat surprisingly\, it can be sh
own that simple sample means of appropriately rand
omized observations are always optimal for estimat
ing linear functionals. Our analysis also allows f
or a quantification of the price of local differen
tial privacy in terms of loss of statistical accur
acy. This price appears to be highly problem depen
dent.
LOCATION:MR12
CONTACT:Dr Sergio Bacallado
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