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Martin Wainwright
Statistical Estimation with Privacy Constraints: How to
characterize the trade-offs?
With data being collected at unprecedented scales, the
interaction between privacy and statistics has become increasingly
important. There are obvious tensions between the requirement of
preserving individual privacy versus that of performing statistical
estimation with aggregated data. How does one formalize and
characterize the associated trade-offs? Working under local
differential privacy—a model in which aspects of the data remain
private even from the statistician—we study the tradeoff between
privacy guarantees and the utility of the resulting statistical
estimators. Our results reveal a surprising phenomenon: privacy
constraints can lead to very different rates for canonical problems
like estimating location parameters, as well as non-parametric density
estimation.
Based on joint work with John Duchi, Stanford and Michael Jordan, UC
Berkeley
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Wolfgang Polonik
Nonparametric Inference for Geometric Objects
Inference for geometric objects such as level sets, ridge lines and integral
curves of densities or regression functions received quite some interest recently.
In this talk we will review some of this recent work and present some new results
about the asymptotic distribution of a plug-in estimator for ridge lines (or filaments).
The derivation of the latter requires a result about the extreme value behavior of
certain non-stationary Gaussian random fields indexed by growing manifolds, which is
discussed also. This extreme value result can be considered as a generalization of some
classical work by Bickel and Rosenblatt (1973) and work by Piterbarg and Stamatovich (2001).
This is joint work with Wanli Qiao, University of California, Davis
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Giulia Cereda
Non parametric Bayesian approach to LR assessment in case of rare type match
The evaluation of a match between the DNA profile of a stain found on a crime scene and that of a suspect
(previously identified) involves the use of the unknown parameter \(\mathbf{p}=(p_1, p_2, ...)\),
(the ordered vector which represents the frequencies of the different DNA profiles in the population
of potential donors) and the names of the different DNA types.
We propose a Bayesian non parametric method which considers \(P\) as a random variable distributed
according to the two-parameter Poisson Dirichlet distribution, and discards the information about
the names of the different DNA types.
The ultimate goal of this model is to evaluate DNA matches in the rare type case, that is the situation
in which the suspect's profile, matching the crime stain profile, is not in the database of reference.
http://arxiv.org/abs/1506.08444
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