Random Sampling Plus Fake Data: Multidimensional Frequency Estimates With Local Differential Privacy
Résumé
With local differential privacy (LDP), users can privatize
their data and thus guarantee privacy properties before
transmitting it to the server (a.k.a. the aggregator). One primary
objective of LDP is frequency (or histogram) estimation, in which
the aggregator estimates the number of users for each possible
value. In practice, when a study with rich content on a population
is desired, the interest is in the multiple attributes of the
population, that is to say, in multidimensional data ($d \geq 2$).
However, contrary to the problem of frequency estimation of a
single attribute (the majority of the works), the multidimensional
aspect imposes to pay particular attention to the privacy budget.
This one can indeed grow extremely quickly due to the composition
theorem. To the authors' knowledge, two solutions seem to stand
out for this task: 1) splitting the privacy budget for each
attribute, i.e., send each value with $\frac{\epsilon}{d}$-LDP
(\textit{Spl}), and 2) random sampling a single attribute and
spend all the privacy budget to send it with $\epsilon$-LDP
(\textit{Smp}). Although \textit{Smp} adds additional sampling
error, it has proven to provide higher data utility than the
former \textit{Spl} solution. However, we argue that aggregators
(who are also seen as attackers) are aware of the sampled
attribute and its LDP value, which is protected by a "less strict"
$\epsilon$ probability bound (rather than $\frac{\epsilon}{d}$).
This way, we propose a solution named \underline{R}andom
\underline{S}ampling plus \underline{F}ake \underline{D}ata
(RS+FD), which allows creating \textit{uncertainty} over the
sampled attribute by generating fake data for each non-sampled
attribute; RS+FD further benefits from amplification by sampling.
We theoretically and experimentally validate our proposed solution
on both synthetic and real-world datasets to show that RS+FD
achieves nearly the same or better utility than the
state-of-the-art \textit{Smp} solution.
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