Cai, Hanqing;
(2024)
High-dimensional Change-point Estimation Under Structural Assumptions.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
Change-point analysis has been successfully applied to detect changes in multivariate and high-dimensional data streams over time. However, many existing methods did not consider the additional structures that data may possess. In this thesis, we study the problem of high-dimensional change-point estimation under structural assumptions. We mainly study two structures: group sparsity structure and network structure. For group sparsity structure, we assume that coordinates in mean vectors are naturally divided into groups and changes only occur in a small subset of groups. We propose groupInspect which uses the group information to estimate a projection direction so as to aggregate information across the component series to estimate the change-point in the mean under this structure. For network structure, we assume that coordinates are connected into a network, and changes start from a source coordinate and then spread out to the neighbouring coordinates. We propose SpreadDetect to estimate the initial time of change as well as the location of the source coordinate of change. For both algorithms, we provide theoretical guarantees on our proposed estimators. We also demonstrate the performance of the two algorithms using simulation studies and real-data examples.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | High-dimensional Change-point Estimation Under Structural Assumptions |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2024. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10191602 |
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