19,535 research outputs found
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
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
Leveraging private capital for climate mitigation: evidence from the clean development mechanism
To mitigate climate change, states must make significant investments into energy and other sectors. To solve this problem, scholars emphasize the importance of leveraging private capital. If states create institutional mechanisms that promote private investment, they can reduce the fiscal cost of carbon abatement. We examine the ability of different international institutional designs to leverage private capital in the context of the Kyoto Protocol's Clean Development Mechanism (CDM). Empirically, we analyze private capital investment in 3749 climate mitigation projects under the CDM, 2003–2011. Since the CDM allows both bilateral and unilateral implementation, we can compare the two modes of contracting within one context. Our model analyzes equilibrium private investment in climate mitigation. When the cost of mitigation is high, unilateral project implementation in one host country, without foreign collaboration, draws more investment than bilateral contracting, whereby foreign investors participate in the project
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
Mechanisms of Endogenous Institutional Change
This paper proposes an analytical-cum-conceptual framework for understanding the nature of institutions as well as their changes. In doing so, it attempts to achieve two things: First, it proposes a way to reconcile an equilibrium (endogenous) view of institutions with the notion of agents’ bounded rationality by introducing such concepts as a summary representation of equilibrium as common knowledge of agents. Second, it specifies some generic mechanisms of institutional coherence and change -- overlapping social embededdness, Schumpeterian innovation in bundling games and dynamic institutional complementarities -- useful for understanding the dynamic interactions of economic, political, social and organizational factors.
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