Solving Schrödinger Bridges via Maximum Likelihood
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 a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/9/1134 |
| _version_ | 1797519456726941696 |
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| author | Francisco Vargas Pierre Thodoroff Austen Lamacraft Neil Lawrence |
| author_facet | Francisco Vargas Pierre Thodoroff Austen Lamacraft Neil Lawrence |
| author_sort | Francisco Vargas |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T07:43:03Z |
| format | Article |
| id | doaj.art-e7b7902e53604e40823e4b77044982a2 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T07:43:03Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-e7b7902e53604e40823e4b77044982a22023-11-22T12:57:06ZengMDPI AGEntropy1099-43002021-08-01239113410.3390/e23091134Solving Schrödinger Bridges via Maximum LikelihoodFrancisco Vargas0Pierre Thodoroff1Austen Lamacraft2Neil Lawrence3The Computer Laboratory, Department of Computer Science and Technology, University of Cambridge, William Gates Building, 15 JJ Thomson Avenue, Cambridge CB3 0FD, UKThe Computer Laboratory, Department of Computer Science and Technology, University of Cambridge, William Gates Building, 15 JJ Thomson Avenue, Cambridge CB3 0FD, UKThe Cavendish Laboratory, Deparment of Physics, The Old Schools, Trinity Ln, Cambridge CB2 1TN, UKThe Computer Laboratory, Department of Computer Science and Technology, University of Cambridge, William Gates Building, 15 JJ Thomson Avenue, Cambridge CB3 0FD, UKThe 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.https://www.mdpi.com/1099-4300/23/9/1134Schrödinger bridgesmachine learningstochastic control |
| spellingShingle | Francisco Vargas Pierre Thodoroff Austen Lamacraft Neil Lawrence Solving Schrödinger Bridges via Maximum Likelihood Entropy Schrödinger bridges machine learning stochastic control |
| title | Solving Schrödinger Bridges via Maximum Likelihood |
| title_full | Solving Schrödinger Bridges via Maximum Likelihood |
| title_fullStr | Solving Schrödinger Bridges via Maximum Likelihood |
| title_full_unstemmed | Solving Schrödinger Bridges via Maximum Likelihood |
| title_short | Solving Schrödinger Bridges via Maximum Likelihood |
| title_sort | solving schrodinger bridges via maximum likelihood |
| topic | Schrödinger bridges machine learning stochastic control |
| url | https://www.mdpi.com/1099-4300/23/9/1134 |
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