Vargas, F., Thodoroff, P., Lamacraft, A. et al. (1 more author) (2021) Solving Schrödinger bridges via maximum likelihood. Entropy, 23 (9). 1134.
Abstract
The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research. Our main contribution is the proof of equivalence between solving the SBP and an autoregressive maximum likelihood estimation objective. This formulation circumvents many of the challenges of density estimation and enables direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 The Authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
Keywords: | Schrödinger bridges; machine learning; stochastic control |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Funding Information: | Funder Grant number Alan Turing Institute N/A |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 Nov 2021 07:23 |
Last Modified: | 17 Nov 2021 07:23 |
Status: | Published |
Publisher: | MDPI AG |
Refereed: | Yes |
Identification Number: | 10.3390/e23091134 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:180518 |
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