Private Decayed Sum Estimation under Continual Observation

TL;DR

This paper develops differentially private algorithms for estimating decayed sums in streaming data, addressing sliding windows, exponential decay, and polynomial decay models, with proven accuracy bounds and lower bounds.

Contribution

It introduces novel private algorithms for decayed sum estimation under continual observation, extending the continual privacy model to new decay settings.

Findings

Algorithms achieve accuracy within $1/\eps$ and polylogarithmic terms.

Lower bounds match the upper bounds within polylog factors.

Polynomial decay algorithms handle partial solution composition challenges.

Abstract

In monitoring applications, recent data is more important than distant data. How does this affect privacy of data analysis? We study a general class of data analyses - computing predicate sums - with privacy. Formally, we study the problem of estimating predicate sums {\em privately}, for sliding windows (and other well-known decay models of data, i.e. exponential and polynomial decay). We extend the recently proposed continual privacy model of Dwork et al. We present algorithms for decayed sum which are $\eps$-differentially private, and are accurate. For window and exponential decay sums, our algorithms are accurate up to additive $1/\eps$ and polylog terms in the range of the computed function; for polynomial decay sums which are technically more challenging because partial solutions do not compose easily, our algorithms incur additional relative error. Further, we show lower bounds, tight within polylog factors and tight with respect to the dependence on the probability of error.