Median regression with differential privacy
This work addresses privacy concerns in robust statistical analysis for datasets requiring individual privacy protection, presenting incremental improvements over existing methods.
The paper tackles median regression with differential privacy by proposing three privacy-preserving algorithms, showing that the first method has better accuracy for small sample sizes, while the second and third methods offer time efficiency advantages as sample size increases.
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.