Euclidean mirrors and first-order changepoints in network time series
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911499369316352 |
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| author | Chen, Tianyi Lubberts, Zachary Athreya, Avanti Park, Youngser Priebe, Carey E. |
| author_facet | Chen, Tianyi Lubberts, Zachary Athreya, Avanti Park, Youngser Priebe, Carey E. |
| contents | We describe a model for a network time series whose evolution is governed by an underlying stochastic process, known as the latent position process, in which network evolution can be represented in Euclidean space by a curve, called the Euclidean mirror. We define the notion of a first-order changepoint for a time series of networks, and construct a family of latent position process networks with underlying first-order changepoints. We prove that a spectral estimate of the associated Euclidean mirror localizes these changepoints, even when the graph distribution evolves continuously, but at a rate that changes. Simulated and real data examples on organoid networks show that this localization captures empirically significant shifts in network evolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11111 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Euclidean mirrors and first-order changepoints in network time series Chen, Tianyi Lubberts, Zachary Athreya, Avanti Park, Youngser Priebe, Carey E. Methodology 62F10, 62J05, 62M15 We describe a model for a network time series whose evolution is governed by an underlying stochastic process, known as the latent position process, in which network evolution can be represented in Euclidean space by a curve, called the Euclidean mirror. We define the notion of a first-order changepoint for a time series of networks, and construct a family of latent position process networks with underlying first-order changepoints. We prove that a spectral estimate of the associated Euclidean mirror localizes these changepoints, even when the graph distribution evolves continuously, but at a rate that changes. Simulated and real data examples on organoid networks show that this localization captures empirically significant shifts in network evolution. |
| title | Euclidean mirrors and first-order changepoints in network time series |
| topic | Methodology 62F10, 62J05, 62M15 |
| url | https://arxiv.org/abs/2405.11111 |