论文标题
具有差异隐私的中间回归
Median regression with differential privacy
论文作者
论文摘要
中位回归分析具有稳健性的属性，与基于平均值的回归相比，它使其具有吸引力，而差异隐私可以在对某些数据集的统计分析期间保护个人隐私。在本文中，提出了三种隐私保存方法以用于中间回归。第一种算法基于有限的平滑方法，第二种算法提供了一种迭代方式，最后一种进一步采用了贪婪的坐标下降方法。证明了这三种方法的隐私保留属性。还提供了这些算法的准确性结合或收敛属性。数值计算表明，当样本量较小时，第一种方法的精度比其他方法更好。当样本量变大时，第一种方法需要更多的时间，而第二种方法则需要更少的时间，匹配精度良好。对于第三种方法，在两种情况下的时间都较小，而高度取决于步长。
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.
