Sun, Zhuo;
(2023)
Transfer learning in Monte Carlo Methods and Beyond.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
From computational statistics to machine learning, many methods have already achieved excellent performance for one single task given a moderate or large number of data points, e.g., kernel methods and deep learning. A task is usually a regression task, a classification task or a Monte Carlo integration task in statistical learning. However, the performance of those methods is likely to degrade when the sample size of the training data is small; when latent information across tasks is ignored; when computational cost is prohibitively expensive. In this thesis, we focus on transfer learning for Monte Carlo methods and beyond via the scope of multi-task learning and meta-learning. It is well known that supervised learning aims to solve a specific task and often requires to train a model on some labeled data points (also known as training set). Monte Carlo methods provide us with estimators of expectations of functions of random variables with respect to some distributions. In this context, it is desirable to design novel algorithms or methods to explore and exploit transferable information across related tasks for both Monte Carlo methods and supervised learning. This thesis includes three novel transfer learning methods. In the first work, we extend existing control variates, a powerful kind of post-processing tools for Monte Carlo methods, and propose a general framework called vector-valued control variates for multiple related integrals. In the second work, inspired by gradient-based meta-learning, we further generalise existing control variates to meta-learning control variates. In the third work, we extend gradient-based meta-learning to be a gradient-based probabilistic learning algorithm for few-shot image classification by introducing latent class prototypes.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Transfer learning in Monte Carlo Methods and Beyond |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2023. 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-pp.ucl.ac.uk/id/eprint/10184443 |
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