Detecting Mutual Excitations in Non-Stationary Hawkes Processes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911382004301824 |
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| author | Mossel, Elchanan Sridhar, Anirudh |
| author_facet | Mossel, Elchanan Sridhar, Anirudh |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_11717 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Detecting Mutual Excitations in Non-Stationary Hawkes Processes Mossel, Elchanan Sridhar, Anirudh Statistics Theory Probability 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. |
| title | Detecting Mutual Excitations in Non-Stationary Hawkes Processes |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2601.11717 |