Differential Privacy for Regularised Linear Regression

We present epsilon-differentially private functional mechanisms for variants of regularised linear regression, LASSO, Ridge, and elastic net. We empirically and comparatively analyse their effectiveness. We quantify the error incurred by these epsilon-differentially private functional mechanisms with respect to the non-private linear regression. We show that the functional mechanism is more effective than the state-of-art differentially private mechanism using input perturbation for the three main regularised linear regression models. We also discuss caveats in the functional mechanism, such as non-convexity of the noisy loss function, which causes instability in the results.