论文标题
在当地差异隐私下的Fisher信息
Fisher information under local differential privacy
论文作者
论文摘要
我们开发了数据处理不平等，这些不平等现象描述了统计样本中的Fisher信息如何在当地差异隐私约束下使用隐私参数$ \ VAREPSILON $扩展。这些边界在一般条件下对统计模型分布的分布有效，并且它们在哪些条件下阐明了对$ \ varepsilon $的依赖性是线性，二次或指数。我们展示了这些不平等意味着高斯位置模型的私人估计和所有隐私级别的离散分配估计$ \ varepsilon> 0 $的私人估计的最佳下限。我们进一步将这些不等式应用于稀疏的Bernoulli模型，并以订单匹配平方$ \ ell^2 $错误演示隐私机制和估计器。
We develop data processing inequalities that describe how Fisher information from statistical samples can scale with the privacy parameter $\varepsilon$ under local differential privacy constraints. These bounds are valid under general conditions on the distribution of the score of the statistical model, and they elucidate under which conditions the dependence on $\varepsilon$ is linear, quadratic, or exponential. We show how these inequalities imply order optimal lower bounds for private estimation for both the Gaussian location model and discrete distribution estimation for all levels of privacy $\varepsilon>0$. We further apply these inequalities to sparse Bernoulli models and demonstrate privacy mechanisms and estimators with order-matching squared $\ell^2$ error.
