Differential Privacy for Stochastic Matrices Using the Matrix Dirichlet Mechanism
Differential Privacy for Stochastic Matrices Using the Matrix Dirichlet Mechanism
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DOI：
10.1109/cdc49753.2023.10383376
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发表时间：
2023-12
期刊：
影响因子：
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通讯作者：
Brandon Fallin;C. Hawkins;Bo Chen;Parham Gohari;Alexander Benvenuti;U. Topcu;Matthew T. Hale
中科院分区：
文献类型：
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作者：
Brandon Fallin;C. Hawkins;Bo Chen;Parham Gohari;Alexander Benvenuti;U. Topcu;Matthew T. Hale
随机矩阵是分析马尔可夫链的常用方法，但如果使用随机矩阵会导致敏感信息的泄露。因此，在本文中，我们引入了一种私有化随机矩阵的技术，其方式(i)隐藏了它们包含的概率，（ii）仍然允许对马尔可夫链进行准确的分析。具体来说，我们使用差分隐私，这是一个保护敏感数据的统计框架。为了实现它，我们引入了矩阵狄利克雷机制，它是一种概率映射，通过扰动随机矩阵来提供隐私。我们证明了这种机制提供了差分隐私，并将私有随机矩阵中引起的误差量化为所提供隐私强度的函数。然后，我们将底层敏感随机矩阵的平稳分布与其私有化形式的平稳分布之间的距离绑定。数值结果表明，在典型条件下，隐私引入的随机矩阵平稳分布误差低至5.05%。
Stochastic matrices are commonly used to analyze Markov chains, but revealing them can leak sensitive information. Therefore, in this paper we introduce a technique to privatize stochastic matrices in a way that (i) conceals the probabilities they contain, and (ii) still allows for accurate analyses of Markov chains. Specifically, we use differential privacy, which is a statistical framework for protecting sensitive data. To implement it, we introduce the Matrix Dirichlet Mechanism, which is a probabilistic mapping that perturbs a stochastic matrix to provide privacy. We prove that this mechanism provides differential privacy, and we quantify the error induced in private stochastic matrices as a function of the strength of privacy being provided. We then bound the distance between the stationary distribution of the underlying, sensitive stochastic matrix and the stationary distribution of its privatized form. Numerical results show that, under typical conditions, privacy introduces error as low as 5.05% in the stationary distribution of a stochastic matrix.