121,613 research outputs found
The Role of Interactivity in Local Differential Privacy
We study the power of interactivity in local differential privacy. First, we
focus on the difference between fully interactive and sequentially interactive
protocols. Sequentially interactive protocols may query users adaptively in
sequence, but they cannot return to previously queried users. The vast majority
of existing lower bounds for local differential privacy apply only to
sequentially interactive protocols, and before this paper it was not known
whether fully interactive protocols were more powerful. We resolve this
question. First, we classify locally private protocols by their
compositionality, the multiplicative factor by which the sum of a
protocol's single-round privacy parameters exceeds its overall privacy
guarantee. We then show how to efficiently transform any fully interactive
-compositional protocol into an equivalent sequentially interactive protocol
with an blowup in sample complexity. Next, we show that our reduction is
tight by exhibiting a family of problems such that for any , there is a
fully interactive -compositional protocol which solves the problem, while no
sequentially interactive protocol can solve the problem without at least an
factor more examples. We then turn our attention to
hypothesis testing problems. We show that for a large class of compound
hypothesis testing problems --- which include all simple hypothesis testing
problems as a special case --- a simple noninteractive test is optimal among
the class of all (possibly fully interactive) tests
Integration of Poland into EU global industrial networks: the evidence and the main challenges
In this paper, we attempt to identify the achievements of one decade of transformation of the Polish economy in effecting the integration of its manufacturing sector with those of the broader European and global economy, using the automotive industry as an illustrative example. We begin with a broad picture of the current situation in Poland, looking particularly at the motivations of EU-based investors. We then discuss the automobile industry, again examining the motives of foreign investors and the effects of policy on their behavior. Next, we examine the chief public and private actors in the integration process, with a particular focus on their roles in trying to push Poland's integration in the direction of high value added and high innovation. Finally, we briefly discuss the impact of Poland's accession to the EU on industrial networking, and then summarize our conclusions and suggest a research framework for testing the hypothesis (formulated on the basis of our observations of the Polish case) that the market orientation of a given industry, measured by the ratio of the trade balance in that industry to its total domestic output, depends among other things on ownership structure, with the domestically-owned sector tending to use locally developed technologies and the foreign-owned sector tending to transfer in technology from abroad
Contraction of Locally Differentially Private Mechanisms
We investigate the contraction properties of locally differentially private
mechanisms. More specifically, we derive tight upper bounds on the divergence
between and output distributions of an
-LDP mechanism in terms of a divergence between the
corresponding input distributions and , respectively. Our first main
technical result presents a sharp upper bound on the -divergence
in terms of and
. We also show that the same result holds for a large family of
divergences, including KL-divergence and squared Hellinger distance. The second
main technical result gives an upper bound on
in terms of total variation distance
and . We then utilize these bounds to
establish locally private versions of the van Trees inequality, Le Cam's,
Assouad's, and the mutual information methods, which are powerful tools for
bounding minimax estimation risks. These results are shown to lead to better
privacy analyses than the state-of-the-arts in several statistical problems
such as entropy and discrete distribution estimation, non-parametric density
estimation, and hypothesis testing
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
Social Learning with Partial Information Sharing
This work addresses the problem of sharing partial information within social
learning strategies. In traditional social learning, agents solve a distributed
multiple hypothesis testing problem by performing two operations at each
instant: first, agents incorporate information from private observations to
form their beliefs over a set of hypotheses; second, agents combine the
entirety of their beliefs locally among neighbors. Within a sufficiently
informative environment and as long as the connectivity of the network allows
information to diffuse across agents, these algorithms enable agents to learn
the true hypothesis. Instead of sharing the entirety of their beliefs, this
work considers the case in which agents will only share their beliefs regarding
one hypothesis of interest, with the purpose of evaluating its validity, and
draws conditions under which this policy does not affect truth learning. We
propose two approaches for sharing partial information, depending on whether
agents behave in a self-aware manner or not. The results show how different
learning regimes arise, depending on the approach employed and on the inherent
characteristics of the inference problem. Furthermore, the analysis
interestingly points to the possibility of deceiving the network, as long as
the evaluated hypothesis of interest is close enough to the truth
Hypothesis Testing in Feedforward Networks with Broadcast Failures
Consider a countably infinite set of nodes, which sequentially make decisions
between two given hypotheses. Each node takes a measurement of the underlying
truth, observes the decisions from some immediate predecessors, and makes a
decision between the given hypotheses. We consider two classes of broadcast
failures: 1) each node broadcasts a decision to the other nodes, subject to
random erasure in the form of a binary erasure channel; 2) each node broadcasts
a randomly flipped decision to the other nodes in the form of a binary
symmetric channel. We are interested in whether there exists a decision
strategy consisting of a sequence of likelihood ratio tests such that the node
decisions converge in probability to the underlying truth. In both cases, we
show that if each node only learns from a bounded number of immediate
predecessors, then there does not exist a decision strategy such that the
decisions converge in probability to the underlying truth. However, in case 1,
we show that if each node learns from an unboundedly growing number of
predecessors, then the decisions converge in probability to the underlying
truth, even when the erasure probabilities converge to 1. We also derive the
convergence rate of the error probability. In case 2, we show that if each node
learns from all of its previous predecessors, then the decisions converge in
probability to the underlying truth when the flipping probabilities of the
binary symmetric channels are bounded away from 1/2. In the case where the
flipping probabilities converge to 1/2, we derive a necessary condition on the
convergence rate of the flipping probabilities such that the decisions still
converge to the underlying truth. We also explicitly characterize the
relationship between the convergence rate of the error probability and the
convergence rate of the flipping probabilities
- …