| Paper ID | D6-S2-T4.1 |
| Paper Title |
Alpha-Information-theoretic Privacy Watchdog and Optimal Privatization Scheme |
| Authors |
Ni Ding, University of Melbourne, Australia; Mohammad Amin Zarrabian, Australian National University, Australia; Parastoo Sadeghi, University of New South Wales, Canberra, Australia |
| Session |
D6-S2-T4: Information Leakage |
| Chaired Session: |
Monday, 19 July, 22:20 - 22:40 |
| Engagement Session: |
Monday, 19 July, 22:40 - 23:00 |
| Abstract |
This paper proposes an $\alpha$-lift measure for data privacy and determines the optimal privatization scheme that minimizes the $\alpha$-lift in the watchdog method. To release useful data $X$ that is correlated with sensitive data $S$, the ratio of the posterior belief to the prior belief on sensitive data with respect to the useful data is called `lift', which quantifies privacy risk. The $\alpha$-lift denoted by $\ell_{\alpha}(x)$ is proposed as the $L_\alpha$-norm of the lift for a given realization $x$. This is a tunable measure: when $\alpha < \infty$, each lift is weighted by its likelihood of appearing in the dataset (w.r.t. the marginal probability $p(s)$); for $\alpha = \infty$, $\alpha$-lift reduces to the existing maximum lift. To generate the sanitized data $Y$, we adopt the privacy watchdog method using $\alpha$-lift: obtain realizations of useful data such that the $\alpha$-lift is greater than a threshold $e^{\eps}$; apply a randomization mechanism to these `high-risk' realizations, while all other realizations of $X$ are published directly. For the resulting $\alpha$-lift denoted by $\ell_{\alpha}(y)$, it is shown that the Sibson mutual information $I_{\alpha}^{S}(S;Y)$ is proportional to $\E[ \ell_{\alpha}(y)]$. We further define a stronger privacy measure denoted $\bar{I}_{\alpha}^{S}(S;Y)$ using the worst-case $\alpha$-lift: $\bar{I}_{\alpha}^{S}(S;Y) \propto \max_{y} \ell_{\alpha}(y)$. We prove that the optimal watchdog randomization that minimizes both $I_{\alpha}^{S}(S;Y)$ and $\bar{I}_{\alpha}^{S}(S;Y)$ is $X$-invariant. Numerical experiments show that $\alpha$-lift can provide flexibility in the privacy-utility tradeoff.
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