Liao, Shujian;
(2022)
Log signatures in machine learning.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
Rough path theory, originated as a branch of stochastic analysis, is an emerging tool for analysing complex sequential data in machine learning with increasing attention. This is owing to the core mathematical object of rough path theory, i.e., the signature/log-signature of a path, which has analytical and algebraic properties. This thesis aims to develop a principled and effective model for time series data based on the log-signature method and the recurrent neural network (RNN). The proposed (generalized) Logsig-RNN model can be regarded as a generalization of the RNN model, which boosts the model performance of the RNN by reducing the time dimension and summarising the local structures of sequential data via the log-signature feature. This hybrid model serves as a generic neural network for a wide range of time series applications. In this thesis, we construct the mathematical formulation for the (generalized) Logsig-RNN model, analyse its complexity and establish the universality. We validate the effectiveness of the proposed method for time series analysis in both supervised learning and generative tasks. In particular, for the skeleton human action recognition tasks, we demonstrates that by replacing the RNN module by the Logsig-RNN in state-of-the-art (SOTA) networks improves the accuracy, efficiency and robustness. In addition, our generator based on the Logsig-RNN model exhibits better performance in generating realistic-looking time series data than classical RNN generators and other baseline methods from the literature. Apart from that, another contribution of our work is to construct a novel Sig-WGAN framework to address the efficiency issue and instability training of traditional generative adversarial networks for time series generation.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Log signatures in machine learning |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2022. 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 > 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 Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10156498 |
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