Privacy-Preserving Statistical Analysis of Genomic Data using Compressive Mechanism with Haar Wavelet Transform

To promote the use of personal genome information in medicine, it is important to analyze the relationship between diseases and the human genomes. Therefore, statistical analysis using genomic data is often conducted, but there is a privacy concern with respect to releasing the statistics as they are. Existing methods to address this problem using the concept of differential privacy cannot provide accurate outputs under strong privacy guarantees, making them less practical. In this study, for the first time we investigate the application of a compressive mechanism to genomic statistical data and propose two approaches. The first is to apply the normal compressive mechanism to the statistics vector along with an algorithm to determine the number of nonzero entries in a sparse representation. The second is to alter the mechanism based on the data, aiming to release significant SNPs with a high probability. In this algorithm, we apply the compressive mechanism with the input as a sparse vector for significant data and the Laplace mechanism for non-significant data. Using the Haar transform for the wavelet matrix in the compressive mechanism is advantageous to determine the number of nonzero elements and the amount of noise. In addition, we theoretically prove that our proposed method achieves{epsilon} -differential privacy. We evaluated our methods in terms of accuracy, rank error, and run time compared to the Laplace and exponential mechanisms. The results show that our second method in particular can guarantee both high privacy assurance as well as utility. The Python implementation of our experiments is available at https://github.com/ay0408/CompLaplace.