# Privacy-Aware Guessing Efficiency

arXiv: https://arxiv.org/abs/1704.03606 · HTML: https://mlsanity.com/paper/1704.03606/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2017.

## Built on by (most cited first, 1 of 1)

- [Summary Statistic Privacy in Data Sharing](https://mlsanity.com/paper/2303.02014/) (2023)

## Abstract (arXiv)

We investigate the problem of guessing a discrete random variable Y under a privacy constraint dictated by another correlated discrete random variable X, where both guessing efficiency and privacy are assessed in terms of the probability of correct guessing. We define h(PXY, ε) as the maximum probability of correctly guessing Y given an auxiliary random variable Z, where the maximization is taken over all PZ|Y ensuring that the probability of correctly guessing X given Z does not exceed ε. We show that the map εmapsto h(PXY, ε) is strictly increasing, concave, and piecewise linear, which allows us to derive a closed form expression for h(PXY, ε) when X and Y are connected via a binary-input binary-output channel. For (Xn, Yn) being pairs of independent and identically distributed binary random vectors, we similarly define underlinehn(PXnYn, ε) under the assumption that Zn is also a binary vector. Then we obtain a closed form expression for underlinehn(PXnYn, ε) for sufficiently large, but nontrivial values of ε.