1,704 research outputs found
Distributed Private Heavy Hitters
In this paper, we give efficient algorithms and lower bounds for solving the
heavy hitters problem while preserving differential privacy in the fully
distributed local model. In this model, there are n parties, each of which
possesses a single element from a universe of size N. The heavy hitters problem
is to find the identity of the most common element shared amongst the n
parties. In the local model, there is no trusted database administrator, and so
the algorithm must interact with each of the parties separately, using a
differentially private protocol. We give tight information-theoretic upper and
lower bounds on the accuracy to which this problem can be solved in the local
model (giving a separation between the local model and the more common
centralized model of privacy), as well as computationally efficient algorithms
even in the case where the data universe N may be exponentially large
Extremal Mechanisms for Local Differential Privacy
Local differential privacy has recently surfaced as a strong measure of
privacy in contexts where personal information remains private even from data
analysts. Working in a setting where both the data providers and data analysts
want to maximize the utility of statistical analyses performed on the released
data, we study the fundamental trade-off between local differential privacy and
utility. This trade-off is formulated as a constrained optimization problem:
maximize utility subject to local differential privacy constraints. We
introduce a combinatorial family of extremal privatization mechanisms, which we
call staircase mechanisms, and show that it contains the optimal privatization
mechanisms for a broad class of information theoretic utilities such as mutual
information and -divergences. We further prove that for any utility function
and any privacy level, solving the privacy-utility maximization problem is
equivalent to solving a finite-dimensional linear program, the outcome of which
is the optimal staircase mechanism. However, solving this linear program can be
computationally expensive since it has a number of variables that is
exponential in the size of the alphabet the data lives in. To account for this,
we show that two simple privatization mechanisms, the binary and randomized
response mechanisms, are universally optimal in the low and high privacy
regimes, and well approximate the intermediate regime.Comment: 52 pages, 10 figures in JMLR 201
Differential Privacy and the Fat-Shattering Dimension of Linear Queries
In this paper, we consider the task of answering linear queries under the
constraint of differential privacy. This is a general and well-studied class of
queries that captures other commonly studied classes, including predicate
queries and histogram queries. We show that the accuracy to which a set of
linear queries can be answered is closely related to its fat-shattering
dimension, a property that characterizes the learnability of real-valued
functions in the agnostic-learning setting.Comment: Appears in APPROX 201
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 the first algorithm that efficiently
releases differentially private answers to of all Boolean conjunctions with 1%
average error. This presents significant progress on a key 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
Differential Privacy for Relational Algebra: Improving the Sensitivity Bounds via Constraint Systems
Differential privacy is a modern approach in privacy-preserving data analysis
to control the amount of information that can be inferred about an individual
by querying a database. The most common techniques are based on the
introduction of probabilistic noise, often defined as a Laplacian parametric on
the sensitivity of the query. In order to maximize the utility of the query, it
is crucial to estimate the sensitivity as precisely as possible.
In this paper we consider relational algebra, the classical language for
queries in relational databases, and we propose a method for computing a bound
on the sensitivity of queries in an intuitive and compositional way. We use
constraint-based techniques to accumulate the information on the possible
values for attributes provided by the various components of the query, thus
making it possible to compute tight bounds on the sensitivity.Comment: In Proceedings QAPL 2012, arXiv:1207.055
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