Differentially Private Regression with Unbounded Covariates
This work addresses privacy-preserving regression for data with unbounded covariates, which is a common scenario in real-world applications, representing an incremental advance over prior methods that required strong bounds on covariates.
The authors tackled the problem of performing differentially private regression with unbounded covariates, providing computationally efficient algorithms for Least Squares Fitting, Binary Regression, and Linear Regression under Gaussian marginals, achieving unbiased estimates up to a scaling factor in cases like logistic regression and SVMs.
We provide computationally efficient, differentially private algorithms for the classical regression settings of Least Squares Fitting, Binary Regression and Linear Regression with unbounded covariates. Prior to our work, privacy constraints in such regression settings were studied under strong a priori bounds on covariates. We consider the case of Gaussian marginals and extend recent differentially private techniques on mean and covariance estimation (Kamath et al., 2019; Karwa and Vadhan, 2018) to the sub-gaussian regime. We provide a novel technical analysis yielding differentially private algorithms for the above classical regression settings. Through the case of Binary Regression, we capture the fundamental and widely-studied models of logistic regression and linearly-separable SVMs, learning an unbiased estimate of the true regression vector, up to a scaling factor.