Order-Invariant Cardinality Estimators Are Differentially Private

Charlie Dickens, Justin Thaler, Daniel Ting

Keywords: streaming algorithms, differential privacy, cardinality estimation, distinct elements

TL;DR: Many widely-used cardinality estimation algorithms satisfy differential privacy.

Abstract:

We consider privacy in the context of streaming algorithms for cardinality estimation.
We show that a large class of algorithms all satisfy $\epsilon$-differential privacy,
so long as (a) the algorithm is combined with a simple
down-sampling procedure, and (b) the input stream cardinality
is $\Omega(k/\epsilon)$. Here, $k$ is a certain parameter of the sketch
that is always at most the sketch size in bits, but is typically much smaller.
We also show that, even with no modification, algorithms in our
class satisfy $(\epsilon, \delta)$-differential privacy,
where $\delta$ falls exponentially with the stream cardinality.
Our analysis applies to essentially all popular cardinality estimation
algorithms, and substantially generalizes and tightens privacy bounds from earlier works.
Our approach is faster and exhibits a better utility-space
tradeoff than prior art.