Differentially Private Iterative Screening Rules for Linear Regression
This work addresses privacy-preserving feature selection in linear models, which is an incremental advancement in the field.
The paper tackles the lack of differentially private screening rules for linear regression by developing the first such rule, finding that an initial version overscreens features but a weakened implementation improves performance.
Linear $L_1$-regularized models have remained one of the simplest and most effective tools in data science. Over the past decade, screening rules have risen in popularity as a way to eliminate features when producing the sparse regression weights of $L_1$ models. However, despite the increasing need of privacy-preserving models for data analysis, to the best of our knowledge, no differentially private screening rule exists. In this paper, we develop the first private screening rule for linear regression. We initially find that this screening rule is too strong: it screens too many coefficients as a result of the private screening step. However, a weakened implementation of private screening reduces overscreening and improves performance.