Differentially Private Model Selection with Penalized and Constrained Likelihood
研究了在差分隐私约束下进行多元线性回归模型选择的方法，通过正则化和随机化使基于惩罚最小二乘或似然的模型选择过程满足差分隐私，并证明了其一致性。
Summary In statistical disclosure control, the goal of data analysis is twofold: the information released must provide accurate and useful statistics about the underlying population of interest, while minimizing the potential for an individual record to be identified. In recent years, the notion of differential privacy has received much attention in theoretical computer science, machine learning and statistics. It provides a rigorous and strong notion of protection for individuals’ sensitive information. A fundamental question is how to incorporate differential privacy in traditional statistical inference procedures. We study model selection in multivariate linear regression under the constraint of differential privacy. We show that model selection procedures based on penalized least squares or likelihood can be made differentially private by a combination of regularization and randomization, and we propose two algorithms to do so. We show that our privacy procedures are consistent under essentially the same conditions as the corresponding non-privacy procedures. We also find that, under differential privacy, the procedure becomes more sensitive to the tuning parameters. We illustrate and evaluate our method by using simulation studies and two real data examples.