Information-Theoretic Privacy-Preserving Schemes Based On Perfect Privacy
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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)≤ϵ, where U denotes the released random variable and ϵ 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.
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