Concentration Bounds for High Sensitivity Functions Through Differential Privacy

TL;DR

This paper explores how differential privacy can establish concentration bounds for high-sensitivity functions in non-adaptive data analysis, extending privacy-based techniques beyond low-sensitivity cases.

Contribution

It demonstrates that differential privacy can be used to prove concentration bounds for high-sensitivity functions in the non-adaptive setting, a novel extension of prior work.

Findings

Differential privacy implies concentration bounds for high-sensitivity functions in non-adaptive analysis.

Extends privacy-based concentration results beyond low-sensitivity functions.

Provides theoretical foundations for privacy-driven analysis of high-sensitivity functions.

Abstract

A new line of work [Dwork et al. STOC 2015], [Hardt and Ullman FOCS 2014], [Steinke and Ullman COLT 2015], [Bassily et al. STOC 2016] demonstrates how differential privacy [Dwork et al. TCC 2006] can be used as a mathematical tool for guaranteeing generalization in adaptive data analysis. Specifically, if a differentially private analysis is applied on a sample S of i.i.d. examples to select a low-sensitivity function f, then w.h.p. f(S) is close to its expectation, although f is being chosen based on the data. Very recently, Steinke and Ullman observed that these generalization guarantees can be used for proving concentration bounds in the non-adaptive setting, where the low-sensitivity function is fixed beforehand. In particular, they obtain alternative proofs for classical concentration bounds for low-sensitivity functions, such as the Chernoff bound and McDiarmid's Inequality. In this work, we set out to examine the situation for functions with high-sensitivity, for which differential privacy does not imply generalization guarantees under adaptive analysis. We show that differential privacy can be used to prove concentration bounds for such functions in the non-adaptive setting.