Privacy-preserving and Optimal Interval Release for Disease Susceptibility

In this paper, we consider the problem of privacy-preserving release of function outputs that take private information as input. Disease susceptibilities are known to be associated with clinical features (e.g., age, sex) as well as genetic features represented by SNPs of individuals. Releasing outputs are not privacy-preserving if the private input can be uniquely identified by probabilistic inference using the outputs. To release useful outputs with preserving privacy, we present a mechanism that releases an interval as output, instead of an output value. We suppose adversaries perform probabilistic inference using released outputs to sharpen the posterior distribution of the target attributes. Then, our mechanism has two significant properties. First, when our mechanism provides the output, the increase of the adversary's posterior on any input attribute is upper-bounded by a prescribed level. Second, under this privacy constraint, the mechanism can provide the narrowest (optimal) interval that includes the true output. Building such a mechanism is often intractable. We formulate the design of the mechanism as a discrete constraint optimization problem so that it is solvable in a practical computation time. We also propose an algorithm to obtain the optimal mechanism based on dynamic programming. After applying our mechanism to release disease susceptibilities of obesity, we demonstrate that our mechanism performs better than existing methods in terms of privacy and utility.