Tao, Jiajie;
Ni, Hao;
Liu, Chong;
(2024)
High Rank Path Development: an approach to learning the filtration of stochastic processes.
In: Globerson, A and Mackey, L and Belgrave, D and Fan, A and Paquet, U and Tomczak, J and Zhang, C, (eds.)
Advances in Neural Information Processing Systems 37 (NeurIPS 2024).
NeurIPS
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Abstract
Since the weak convergence for stochastic processes does not account for the growth of information over time which is represented by the underlying filtration, a slightly erroneous stochastic model in weak topology may cause huge loss in multi-periods decision making problems. To address such discontinuities, Aldous introduced the extended weak convergence, which can fully characterise all essential properties, including the filtration, of stochastic processes; however, it was considered to be hard to find efficient numerical implementations. In this paper, we introduce a novel metric called High Rank PCF Distance (HRPCFD) for extended weak convergence based on the high rank path development method from rough path theory, which also defines the characteristic function for measure-valued processes. We then show that such HRPCFD admits many favourable analytic properties which allows us to design an efficient algorithm for training HRPCFD from data and construct the HRPCF-GAN by using HRPCFD as the discriminator for conditional time series generation. Our numerical experiments on both hypothesis testing and generative modelling validate the out-performance of our approach compared with several state-of-the-art methods, highlighting its potential in broad applications of synthetic time series generation and in addressing classic financial and economic challenges, such as optimal stopping or utility maximisation problems. Code is available at https://github.com/DeepIntoStreams/High-Rank-PCF-GAN.git.
| Type: | Proceedings paper |
|---|---|
| Title: | High Rank Path Development: an approach to learning the filtration of stochastic processes |
| Event: | 38th Conference on Neural Information Processing Systems (NeurIPS 2024) |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://proceedings.neurips.cc/paper_files/paper/2... |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| 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 Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10205301 |
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