Differential Privacy without Sensitivity
Differential Privacy without Sensitivity
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发表时间：
2016
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通讯作者：
Kentaro Minami;Hiromi Arai;Issei Sato;Hiroshi Nakagawa
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作者：
Kentaro Minami;Hiromi Arai;Issei Sato;Hiroshi Nakagawa
指数机制是一种构造满足$（\vareps，0）$-差分隐私的随机估计的一般方法。最近，Wang等人表明，吉布斯后验（Gibbs posterior）是一种包含贝叶斯后验的数据依赖概率分布，在损失函数的某些有界条件下，它本质上等同于指数机制。虽然指数机制提供了一种构建$（\vareprom，0）$-差分私有算法的方法，但它需要损失函数的有界性，这对于某些学习问题来说是非常严格的。本文研究了具有凸损失函数和Lipschitz损失函数的Gibbs后验概率的$（\vareprogram，\delta）$-微分隐私问题。我们的结果扩展了经典的指数机制，允许损失函数具有无界的灵敏度。
The exponential mechanism is a general method to construct a randomized estimator that satisfies $(\varepsilon, 0)$-differential privacy. Recently, Wang et al. showed that the Gibbs posterior, which is a data-dependent probability distribution that contains the Bayesian posterior, is essentially equivalent to the exponential mechanism under certain boundedness conditions on the loss function. While the exponential mechanism provides a way to build an $(\varepsilon, 0)$-differential private algorithm, it requires boundedness of the loss function, which is quite stringent for some learning problems. In this paper, we focus on $(\varepsilon, \delta)$-differential privacy of Gibbs posteriors with convex and Lipschitz loss functions. Our result extends the classical exponential mechanism, allowing the loss functions to have an unbounded sensitivity.