Differentially Private Estimation via Statistical Depth
- URL: http://arxiv.org/abs/2207.12602v1
- Date: Tue, 26 Jul 2022 01:59:07 GMT
- Title: Differentially Private Estimation via Statistical Depth
- Authors: Ryan Cumings-Menon
- Abstract summary: Two notions of statistical depth are used to motivate new approximate DP location and regression estimators.
To avoid requiring that users specify a priori bounds on the estimates and/or the observations, variants of these DP mechanisms are described.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Constructing a differentially private (DP) estimator requires deriving the
maximum influence of an observation, which can be difficult in the absence of
exogenous bounds on the input data or the estimator, especially in high
dimensional settings. This paper shows that standard notions of statistical
depth, i.e., halfspace depth and regression depth, are particularly
advantageous in this regard, both in the sense that the maximum influence of a
single observation is easy to analyze and that this value is typically low.
This is used to motivate new approximate DP location and regression estimators
using the maximizers of these two notions of statistical depth. A more
computationally efficient variant of the approximate DP regression estimator is
also provided. Also, to avoid requiring that users specify a priori bounds on
the estimates and/or the observations, variants of these DP mechanisms are
described that satisfy random differential privacy (RDP), which is a relaxation
of differential privacy provided by Hall, Wasserman, and Rinaldo (2013). We
also provide simulations of the two DP regression methods proposed here. The
proposed estimators appear to perform favorably relative to the existing DP
regression methods we consider in these simulations when either the sample size
is at least 100-200 or the privacy-loss budget is sufficiently high.
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