在非稳态Hawkes过程中检测相互激发
Detecting Mutual Excitations in Non-Stationary Hawkes Processes
AI总结：
该研究提出了一种在非稳态Hawkes过程中高效重建稀疏依赖图的算法，适用于时间变化基线速率和非移不变延迟核的情况。
摘要：
我们考虑在非稳态、多变量Hawkes过程中学习相互激发网络（即依赖图）的问题。我们考虑一个一般性设置，其中每个节点的基线速率随时间变化，延迟核不是移不变的。我们的主要结果表明，如果n变量Hawkes过程的依赖图是稀疏的（即其最大度数与n成比例），则我们的算法在观察Hawkes过程时间为T=polylog(n)后，以高概率准确重建该图。我们的算法计算效率高，并且即使只观察到部分时间序列且事件时间不精确时，也能证明成功学习依赖关系。
英文摘要：
We consider the problem of learning the network of mutual excitations (i.e., the dependency graph) in a non-stationary, multivariate Hawkes process. We consider a general setting where baseline rates at each node are time-varying and delay kernels are not shift-invariant. Our main results show that if the dependency graph of an $n$-variate Hawkes process is sparse (i.e., it has a maximum degree that is bounded with respect to $n$), our algorithm accurately reconstructs it from data after observing the Hawkes process for $T = \mathrm{polylog}(n)$ time, with high probability. Our algorithm is computationally efficient, and provably succeeds in learning dependencies even if only a subset of time series are observed and event times are not precisely known.
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