Abstract. Following the publication of an attack on genome-wide association studies (GWAS) data proposed by Homer et al., considerable attention has been given to developing methods for releasing GWAS data in a privacy-preserving way. Here, we develop an end-to-end differentially private method for solving regression problems with convex penalty functions and selecting the penalty parameters by cross-validation. In particular, we focus on penalized logistic regression with elastic-net regularization, a method widely used to in GWAS analyses to identify diseasecausing genes. We show how a differentially private procedure for penalized logistic regression with elastic-net regularization can be applied to the analysis of GWAS data and evaluate our method's performance.
Yu et al. REF solved the problem of differentially private penalized logistic regression with elastic-net regularization by extending the objective perturbation technique to any convex penalty function.
Differentially-Private Logistic Regression for Detecting Multiple-SNP Association in GWAS Databases
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Computer Science Mathematics