Sellier, Jeremy;
(2024)
Efficient Spatial and Temporal Learning with Sparse Spectral Gaussian Processes.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
Gaussian Processes (GPs) have gained substantial attention within the fields of statistics and machine learning. Rooted in Bayesian principles, their appeal lies in their ability to provide a robust framework for conducting inference. Particularly, GPs excel in their ability to capture intricate data dependencies and offer a comprehensive representation of predictive uncertainty. However, as datasets grow in size and complexity, Bayesian nonparametric models employing GPs face notable challenges. A key concern revolves around conducting inference for models with intractable likelihoods, including cases where the likelihoods cannot be feasibly evaluated. Furthermore, a practical challenge arises from the substantial computational demands associated with GPs, characterized by a cubic time complexity, making them less suitable for large datasets. Two prominent examples of these challenges are particularly evident. First, in the case of Poisson process likelihoods used in spatial statistics, where likelihood computations involve the intractable integration of a random function across the input space. Secondly, in time series analysis, while GPs generalizes traditional linear models, their integration into Bayesian change point detection framework (BOCPD) exposes a notable limitation: a naive implementation incurs O(n5) complexity. In both these scenarios, the ability to conduct efficient inference, accurately discern underlying patterns, and seamlessly adapt to scaling demands becomes paramount. This thesis focuses on advancing efficient and adaptable inference methods using GPs for spatial data analysis and time series change point detection. A central emphasis lies in exploring the underutilized potential of reduced-rank GPs, derived from the spectral properties of their kernel, within these domains. This sparse spectral representation of GPs provides significant computational benefits and introduces novel perspectives for addressing complex data inference challenges in these fields.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Efficient Spatial and Temporal Learning with Sparse Spectral Gaussian Processes |
| 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. |
| Keywords: | Bayesian nonparametrics, Point processes, Change point detection |
| 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/10189547 |
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