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Smooth sensitivity and sampling in private data analysis
TLDR
This is the first formal analysis of the effect of instance-based noise in the context of data privacy, and shows how to do this efficiently for several different functions, including the median and the cost of the minimum spanning tree.
What Can We Learn Privately?
TLDR
This work investigates learning algorithms that satisfy differential privacy, a notion that provides strong confidentiality guarantees in the contexts where aggregate information is released about a database containing sensitive information about individuals.
Analyzing Graphs with Node Differential Privacy
TLDR
A generic, efficient reduction is derived that allows us to apply any differentially private algorithm for bounded-degree graphs to an arbitrary graph, based on analyzing the smooth sensitivity of the 'naive' truncation that simply discards nodes of high degree.
Private Analysis of Graph Structure
TLDR
This work extends the approach of Nissim et al. to a new class of statistics, namely k-star queries, and gives hardness results indicating that the approach used for triangles cannot easily be extended to k-triangles.
Monotonicity testing over general poset domains
TLDR
It is shown that in its most general setting, testing that Boolean functions are close to monotone is equivalent, with respect to the number of required queries, to several other testing problems in logic and graph theory.
Some 3CNF properties are hard to test
TLDR
It is proved that there are 3CNF properties that require a linear number of queries, even for adaptive tests, which contrasts with 2C NF properties that are testable with O(√n) queries.
Strong Lower Bounds for Approximating Distribution Support Size and the Distinct Elements Problem
TLDR
The problem of approximating the support size of a distribution from a small number of samples, when each element in the distribution appears with probability at least 1/n is considered, and a nearly linear in n lower bound on the query complexity is proved.
Approximation algorithms for spanner problems and Directed Steiner Forest
TLDR
An O(nlogn)-approximation algorithm for the problem of finding the sparsest spanner of a given directed graph G on n vertices is presented and the approximation ratio almost matches Dinitz and [email protected]?s lower bound for the integrality gap of a natural linear programming relaxation.
Improved Testing Algorithms for Monotonicity
TLDR
Improved algorithms for testing monotonicity of functions are presented, given the ability to query an unknown function f: Σ n ↦ Ξ, and the test always accepts a monotone f, and rejects f with high probability if it is e-far from being monotones.
Transitive-Closure Spanners
TLDR
The common task implicitly tackled in these diverse applications as the problem of constructing sparse TC-spanners is abstracted asThe study of approximability of the size of the sparsest of a given directed graph is initiated.
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