[Busec] Moritz Hardt differential privacy talk on Friday

Sharon Goldberg goldbe at cs.bu.edu
Mon Mar 28 12:08:51 EDT 2011


Hi all,

Another talk about differential privacy in the BU Theory seminar on
Friday 3PM in MCS135.  This is by my academic sibling, Moritz Hardt.

See you there,
Sharon

******

Title: Privately Releasing Conjunctions and the Statistical Query Barrier

Suppose we would like to know all answers to a set of statistical
queries C on a data set up to small error, but we can only access the data
itself using statistical queries. A trivial solution is to exhaustively ask all
queries in C. Can we do any better?

We show that the number of statistical queries necessary and
 sufficient for this task is---up to polynomial factors---equal to the
 agnostic learning complexity of C in Kearns' statistical query (SQ)
 model. This gives a complete answer to the question when running time
 is not a concern.

We then show that the problem can be solved efficiently (allowing arbitrary
 error on a small fraction of queries) whenever the answers to C can be
 described by a submodular function. This includes many natural concept
 classes, such as graph cuts and Boolean disjunctions and conjunctions.

While interesting from a learning theoretic point of view, our main
applications are in privacy-preserving data analysis:

Here, our second result leads to an algorithm that efficiently releases
differentially private answers to all Boolean conjunctions with 1%
average error. This makes progress on an important open problem
in privacy-preserving data analysis.

Our first result on the other hand gives unconditional lower bounds
on any differentially private algorithm that admits a (potentially
non-privacy-preserving) implementation using only statistical queries.
Not only our algorithms, but also most known private algorithms
can be implemented using only statistical queries, and hence are
constrained by these lower bounds. Our result therefore isolates the
complexity of agnostic learning in the SQ-model as a new barrier in the
design of differentially private algorithms.

Joint work with Anupam Gupta, Aaron Roth and Jon Ullman.



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