Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Private Quantiles Estimation in the Presence of Atoms   We address the differentially private estimation of multiple quantiles (MQ)
of a dataset, a key building block in modern data analysis. We apply the recent
non-smoothed Inverse Sensitivity (IS) mechanism to this specific problem and
establish that the resulting method is closely related to the current
state-of-the-art, the JointExp algorithm, sharing in particular the same
computational complexity and a similar efficiency. However, we demonstrate both
theoretically and empirically that (non-smoothed) JointExp suffers from an
important lack of performance in the case of peaked distributions, with a
potentially catastrophic impact in the presence of atoms. While its smoothed
version would allow to leverage the performance guarantees of IS, it remains an
open challenge to implement. As a proxy to fix the problem we propose a simple
and numerically efficient method called Heuristically Smoothed JointExp
(HSJointExp), which is endowed with performance guarantees for a broad class of
distributions and achieves results that are orders of magnitude better on
problematic datasets.

11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th