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CATEGORIES:Statistics
SUMMARY:M-estimation\, noisy optimization and user-level l
ocal privacy - Marco Avella Medina (Columbia Unive
rsity)
DTSTART;TZID=Europe/London:20240202T140000
DTEND;TZID=Europe/London:20240202T150000
UID:TALK209545AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/209545
DESCRIPTION:We propose a general optimization-based framework
for computing differentially private M-estimators.
We first show that robust statistics can be used
in conjunction with noisy gradient descent or nois
y Newton methods in order to obtain optimal privat
e estimators with global linear or quadratic conve
rgence\, respectively. We establish local and glob
al convergence guarantees\, under both local stron
g convexity and self-concordance\, showing that ou
r private estimators converge with high probabilit
y to a small neighborhood of the nonprivate M-esti
mators. We then extend this optimization framework
to the more restrictive setting of local differen
tial privacy (LDP) where a group of users communic
ates with an untrusted central server. Contrary to
most works that aim to protect a single data poin
t\, here we assume each user possesses multiple da
ta points and focus on user-level privacy which ai
ms to protect the entire set of data points belong
ing to a user. Our main algorithm is a noisy gradi
ent descent algorithm\, combined with a user-level
LDP mean estimation procedure to privately comput
e the average gradient across users at each step.
We will highlight the challenges associated with g
uaranteeing user-level LDP and present finite samp
le global linear convergence guarantees for the it
erates of our algorithm.
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Dr Sergio Bacallado
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