1,377 research outputs found
On the Anonymization of Differentially Private Location Obfuscation
Obfuscation techniques in location-based services (LBSs) have been shown
useful to hide the concrete locations of service users, whereas they do not
necessarily provide the anonymity. We quantify the anonymity of the location
data obfuscated by the planar Laplacian mechanism and that by the optimal
geo-indistinguishable mechanism of Bordenabe et al. We empirically show that
the latter provides stronger anonymity than the former in the sense that more
users in the database satisfy k-anonymity. To formalize and analyze such
approximate anonymity we introduce the notion of asymptotic anonymity. Then we
show that the location data obfuscated by the optimal geo-indistinguishable
mechanism can be anonymized by removing a smaller number of users from the
database. Furthermore, we demonstrate that the optimal geo-indistinguishable
mechanism has better utility both for users and for data analysts.Comment: ISITA'18 conference pape
A combinatorial approach to jumping particles
In this paper we consider a model of particles jumping on a row of cells,
called in physics the one dimensional totally asymmetric exclusion process
(TASEP). More precisely we deal with the TASEP with open or periodic boundary
conditions and with two or three types of particles. From the point of view of
combinatorics a remarkable feature of this Markov chain is that it involves
Catalan numbers in several entries of its stationary distribution. We give a
combinatorial interpretation and a simple proof of these observations. In doing
this we reveal a second row of cells, which is used by particles to travel
backward. As a byproduct we also obtain an interpretation of the occurrence of
the Brownian excursion in the description of the density of particles on a long
row of cells.Comment: 24 figure
The importance of better models in stochastic optimization
Standard stochastic optimization methods are brittle, sensitive to stepsize
choices and other algorithmic parameters, and they exhibit instability outside
of well-behaved families of objectives. To address these challenges, we
investigate models for stochastic minimization and learning problems that
exhibit better robustness to problem families and algorithmic parameters. With
appropriately accurate models---which we call the aProx family---stochastic
methods can be made stable, provably convergent and asymptotically optimal;
even modeling that the objective is nonnegative is sufficient for this
stability. We extend these results beyond convexity to weakly convex
objectives, which include compositions of convex losses with smooth functions
common in modern machine learning applications. We highlight the importance of
robustness and accurate modeling with a careful experimental evaluation of
convergence time and algorithm sensitivity
Mean Estimation from Adaptive One-bit Measurements
We consider the problem of estimating the mean of a normal distribution under
the following constraint: the estimator can access only a single bit from each
sample from this distribution. We study the squared error risk in this
estimation as a function of the number of samples and one-bit measurements .
We consider an adaptive estimation setting where the single-bit sent at step
is a function of both the new sample and the previous acquired bits.
For this setting, we show that no estimator can attain asymptotic mean squared
error smaller than times the variance. In other words,
one-bit restriction increases the number of samples required for a prescribed
accuracy of estimation by a factor of at least compared to the
unrestricted case. In addition, we provide an explicit estimator that attains
this asymptotic error, showing that, rather surprisingly, only times
more samples are required in order to attain estimation performance equivalent
to the unrestricted case
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