马尔可夫链状态轨迹的差分隐私
Differential Privacy for Markov Chain State Trajectories
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中文总结 AI 辅助
该研究针对马尔可夫链状态轨迹的隐私泄露问题，提出一种在线差分隐私框架，通过最小化最短路径总边权重生成私有轨迹，实验显示其在3-差分隐私下熵降最多80%，能兼顾隐私与数据实用性。
中文摘要 AI 辅助
数据驱动系统的运行可能需要马尔可夫链的状态轨迹，因为这些轨迹包含对系统有用的信息，例如产品的信用风险、用户的物理位置或用户的互联网浏览行为。然而，共享此类状态轨迹可能会泄露用户的敏感信息，这构成了隐私威胁。因此，我们开发了一种新的框架，用于使用差分隐私对马尔可夫链中的状态轨迹进行私有化。我们的框架在线对状态轨迹进行私有化，即私有状态轨迹与它所近似的敏感状态轨迹同时生成。我们将马尔可夫链视为加权有向图，其边权重是转移概率的负对数。然后，通过最小化私有状态轨迹中每个状态与敏感状态轨迹对应状态的距离来选择该状态，其中距离的概念等于最短路径上的总边权重。我们证明，在高概率下，私有状态轨迹与敏感状态轨迹保持接近，这为私有数据的下游使用维持了高实用性。此外，我们证明，私有状态轨迹始终处于底层马尔可夫链生成的状态轨迹的典型集中，这意味着私有状态轨迹具有与底层马尔可夫链产生的实际状态轨迹相似的统计特性。数值模拟表明，在3-差分隐私下，我们引入的机制与现有技术相比，熵最多降低80%，这说明我们框架生成的私有状态轨迹在保持相同隐私水平的同时，与对应的敏感状态轨迹更为相似。
英文摘要
Data-driven systems may require state trajectories of Markov chains to function because these trajectories contain information that is useful to the system, e.g., a product's credit risk, a user's physical location, or a user's internet browsing behavior. However, sharing such state trajectories can reveal sensitive information about users, which presents a privacy threat. Therefore, we develop a new framework for privatizing the state trajectories in a Markov chain using differential privacy. Our framework privatizes state trajectories online, in the sense that a private state trajectory is generated at the same time as the sensitive one it approximates. We treat Markov chains as weighted directed graphs whose edge weights are the negative logarithms of the transition probabilities. Then, each state in a private state trajectory is chosen by minimizing its distance to the corresponding state in the sensitive state trajectory, where the notion of distance is equal to the total edge weight along a shortest path. We prove that with high probability the private state trajectory remains close to the sensitive one, which maintains high utility for downstream uses of private data. Additionally, we prove that private state trajectories are consistently in the typical set of state trajectories generated by the underlying Markov chain, which means that private state trajectories have similar statistical properties to actual state trajectories produced by the underlying Markov chain. Numerical simulations show that under $3$-differential privacy, the mechanism we introduce exhibits up to an $80\%$ decrease in entropy compared to the state of the art, which illustrates that private state trajectories generated by our framework more closely resemble their corresponding sensitive state trajectory while maintaining the same level of privacy.
