论文标题
私人学习霍克斯流程
Differentially Private Learning of Hawkes Processes
论文作者
论文摘要
霍克斯流程最近从机器学习社区中引起了人们对建模事件序列数据的多功能性的越来越多的关注。尽管它们具有悠久的历史可以追溯到几十年，但其某些属性（例如学习参数的样本复杂性和释放差异化私有版本）尚待进行彻底分析。在这项工作中，我们研究了具有背景强度$μ$和激发功能$αe^{ - βT} $的标准鹰队过程。我们提供$μ$和$ a $的非私有和差异私人估计器，并在两种设置中获得样本复杂性，以量化隐私成本。我们的分析利用了霍克斯过程的强大混合特性和经典的中央限制定理结果，结果较弱的随机变量。我们在合成数据集和真实数据集上验证了理论发现。
Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as sample complexity for learning the parameters and releasing differentially private versions, are yet to be thoroughly analyzed. In this work, we study standard Hawkes processes with background intensity $μ$ and excitation function $αe^{-βt}$. We provide both non-private and differentially private estimators of $μ$ and $α$, and obtain sample complexity results in both settings to quantify the cost of privacy. Our analysis exploits the strong mixing property of Hawkes processes and classical central limit theorem results for weakly dependent random variables. We validate our theoretical findings on both synthetic and real datasets.
