Median regression with differential privacy

TL;DR

This paper introduces three novel privacy-preserving median regression algorithms, analyzing their privacy guarantees, accuracy, and efficiency, with practical comparisons showing their strengths depending on sample size and computational constraints.

Contribution

It proposes three new differential privacy methods for median regression, providing theoretical guarantees and empirical performance analysis.

Findings

First method has better accuracy with small samples.

Second method is faster with larger samples.

Third method is computationally efficient but sensitive to step size.

Abstract

Median regression analysis has robustness properties which make it attractive compared with regression based on the mean, while differential privacy can protect individual privacy during statistical analysis of certain datasets. In this paper, three privacy preserving methods are proposed for median regression. The first algorithm is based on a finite smoothing method, the second provides an iterative way and the last one further employs the greedy coordinate descent approach. Privacy preserving properties of these three methods are all proved. Accuracy bound or convergence properties of these algorithms are also provided. Numerical calculation shows that the first method has better accuracy than the others when the sample size is small. When the sample size becomes larger, the first method needs more time while the second method needs less time with well-matched accuracy. For the third method, it costs less time in both cases, while it highly depends on step size.