J. Goseling and M.N.M. van Lieshout's Contribution to the Discussion of ‘Gaussian Differential Privacy’ by Donget al.
本文讨论高斯差分隐私在官方统计中的应用，指出基于表格保护的主题地图过于保守，提出使用核加权平均生成平滑地图，但需注意攻击者可能通过线性系统反推原始数据。
We congratulate Professors Dong, Roth and Su on their compelling work on Gaussian Differential Privacy. In official statistics, the p%-rule (Hundepoel et al., 2012) is widely used to protect tabular data. In recent work (Hut et al., 2020) we adapted this concept to thematic maps, for example, of energy consumption per company. Usually such maps are drawn directly from an underlying table that is protected from disclosure. The resulting colour-coded map, however, is, by construction, discretised in regions defined by the cells in the table. These geographic regions are usually large, corresponding, for instance, to municipalities. The resulting protection is very conservative, leading to a map with reduced utility. Therefore, there is a need for smooth thematic maps. One might use the Nadaraya–Watson kernel weighted average. This procedure, however, is not necessarily safe. Indeed, suppose that an attacker is able to read off the plotted, smoothed, values of the variables of interest at all measurement locations. Then their original values satisfy a linear system which in many cases (including that of a Gaussian kernel) can be solved exactly if the measurement locations are distinct.