Mechanisms for Hiding Sensitive Genotypes with Information-Theoretic Privacy

TL;DR

This paper proposes an information-theoretic privacy mechanism for genomic data sharing that ensures sensitive genotypes remain hidden while maximizing data utility, addressing privacy leakage issues and computational complexity.

Contribution

It introduces a novel erasure-based privacy mechanism with perfect privacy guarantees and develops efficient algorithms for sequences modeled by hidden Markov models.

Findings

Mechanism guarantees perfect privacy by making released data independent of sensitive genotypes.

Provides an NP-hardness proof for optimal sequence position ordering.

Develops polynomial-time algorithms for hidden Markov model sequences.

Abstract

Motivated by the growing availability of personal genomics services, we study an information-theoretic privacy problem that arises when sharing genomic data: a user wants to share his or her genome sequence while keeping the genotypes at certain positions hidden, which could otherwise reveal critical health-related information. A straightforward solution of erasing (masking) the chosen genotypes does not ensure privacy, because the correlation between nearby positions can leak the masked genotypes. We introduce an erasure-based privacy mechanism with perfect information-theoretic privacy, whereby the released sequence is statistically independent of the sensitive genotypes. Our mechanism can be interpreted as a locally-optimal greedy algorithm for a given processing order of sequence positions, where utility is measured by the number of positions released without erasure. We show that finding an optimal order is NP-hard in general and provide an upper bound on the optimal utility. For sequences from hidden Markov models, a standard modeling approach in genetics, we propose an efficient algorithmic implementation of our mechanism with complexity polynomial in sequence length. Moreover, we illustrate the robustness of the mechanism by bounding the privacy leakage from erroneous prior distributions. Our work is a step towards more rigorous control of privacy in genomic data sharing.