Consider a pair of random variables $(X,Y)$ distributed according to a given joint distribution $p_{XY}$. A curator wishes to maximally disclose information about $Y$, while limiting the information leakage incurred on $X$. Adopting mutual information to measure both utility and privacy of this information disclosure, the problem is to maximize $I(Y;U)$, subject to $I(X;U)\leq\epsilon$, where $U$ denotes the released random variable and $\epsilon$ is a given privacy threshold. Two settings are considered, where in the first one, the curator has access to $(X,Y)$, and hence, the optimization is over $p_{U|XY}$, while in the second one, the curator can only observe $Y$ and the optimization is over $p_{U|Y}$. In both settings, the utility-privacy trade-off is investigated from theoretical and practical perspective. More specifically, several privacy-preserving schemes are proposed in these settings based on generalizing the notion of statistical independence. Moreover, closed-form solutions are provided in certain scenarios. Finally, convexity arguments are provided for the utility-privacy trade-off as functionals of the joint distribution $p_{XY}$.
翻译:一位馆长希望最大限度地披露有关美元的信息,同时限制对美元的信息泄漏。 采用相互信息以衡量这一信息披露的效用和隐私性,问题是最大限度地使用I(Y;U)美元,但以美元(X;U)\leq\epsilon$为限。 在这两种情况下,从理论和实践角度对公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公用-公制-公用-公用-公用-公用-公用-公制-公用-公用-公用-公制-公用-公用-公用-公用-公用-公用-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-公制-提供-提供-制-公制-提供-提供-提供-公制-公制-公制-提供-提供-提供-公制-提供-公制-公制-制-制-