Sparse Private LASSO Logistic Regression
This work addresses the need for sparse, private logistic regression in domains like healthcare or finance where feature selection and privacy are critical, though it is incremental as it builds on existing private LASSO methods.
The paper tackled the problem of differentially private LASSO logistic regression producing dense solutions, which reduces the utility of feature selection, by developing a method that maintains sparse solutions with hard zeros, achieving competitive performance on synthetic and real-world datasets.
LASSO regularized logistic regression is particularly useful for its built-in feature selection, allowing coefficients to be removed from deployment and producing sparse solutions. Differentially private versions of LASSO logistic regression have been developed, but generally produce dense solutions, reducing the intrinsic utility of the LASSO penalty. In this paper, we present a differentially private method for sparse logistic regression that maintains hard zeros. Our key insight is to first train a non-private LASSO logistic regression model to determine an appropriate privatized number of non-zero coefficients to use in final model selection. To demonstrate our method's performance, we run experiments on synthetic and real-world datasets.