Symbolic expression generation via variational auto-encoder
There are many problems in physics, biology, and other natural sciences in which symbolic regression can provide valuable insights and discover new laws of nature. Widespread deep neural networks do not provide interpretable solutions. Meanwhile, symbolic expressions give us a clear relation between...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
PeerJ Inc.
2023-03-01
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| Series: | PeerJ Computer Science |
| Subjects: | |
| Online Access: | https://peerj.com/articles/cs-1241.pdf |
| _version_ | 1811155609976832000 |
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| author | Sergei Popov Mikhail Lazarev Vladislav Belavin Denis Derkach Andrey Ustyuzhanin |
| author_facet | Sergei Popov Mikhail Lazarev Vladislav Belavin Denis Derkach Andrey Ustyuzhanin |
| author_sort | Sergei Popov |
| collection | DOAJ |
| description | There are many problems in physics, biology, and other natural sciences in which symbolic regression can provide valuable insights and discover new laws of nature. Widespread deep neural networks do not provide interpretable solutions. Meanwhile, symbolic expressions give us a clear relation between observations and the target variable. However, at the moment, there is no dominant solution for the symbolic regression task, and we aim to reduce this gap with our algorithm. In this work, we propose a novel deep learning framework for symbolic expression generation via variational autoencoder (VAE). We suggest using a VAE to generate mathematical expressions, and our training strategy forces generated formulas to fit a given dataset. Our framework allows encoding apriori knowledge of the formulas into fast-check predicates that speed up the optimization process. We compare our method to modern symbolic regression benchmarks and show that our method outperforms the competitors under noisy conditions. The recovery rate of SEGVAE is 65% on the Ngyuen dataset with a noise level of 10%, which is better than the previously reported SOTA by 20%. We demonstrate that this value depends on the dataset and can be even higher. |
| first_indexed | 2024-04-10T04:37:19Z |
| format | Article |
| id | doaj.art-51faf45d794541d186fcbec567cc31ec |
| institution | Directory Open Access Journal |
| issn | 2376-5992 |
| language | English |
| last_indexed | 2024-04-10T04:37:19Z |
| publishDate | 2023-03-01 |
| publisher | PeerJ Inc. |
| record_format | Article |
| series | PeerJ Computer Science |
| spelling | doaj.art-51faf45d794541d186fcbec567cc31ec2023-03-09T15:05:08ZengPeerJ Inc.PeerJ Computer Science2376-59922023-03-019e124110.7717/peerj-cs.1241Symbolic expression generation via variational auto-encoderSergei Popov0Mikhail Lazarev1Vladislav Belavin2Denis Derkach3Andrey Ustyuzhanin4Department of Computer Science, Higher School of Economics, Moscow, RussiaDepartment of Computer Science, Higher School of Economics, Moscow, RussiaDepartment of Computer Science, Higher School of Economics, Moscow, RussiaDepartment of Computer Science, Higher School of Economics, Moscow, RussiaDepartment of Computer Science, Higher School of Economics, Moscow, RussiaThere are many problems in physics, biology, and other natural sciences in which symbolic regression can provide valuable insights and discover new laws of nature. Widespread deep neural networks do not provide interpretable solutions. Meanwhile, symbolic expressions give us a clear relation between observations and the target variable. However, at the moment, there is no dominant solution for the symbolic regression task, and we aim to reduce this gap with our algorithm. In this work, we propose a novel deep learning framework for symbolic expression generation via variational autoencoder (VAE). We suggest using a VAE to generate mathematical expressions, and our training strategy forces generated formulas to fit a given dataset. Our framework allows encoding apriori knowledge of the formulas into fast-check predicates that speed up the optimization process. We compare our method to modern symbolic regression benchmarks and show that our method outperforms the competitors under noisy conditions. The recovery rate of SEGVAE is 65% on the Ngyuen dataset with a noise level of 10%, which is better than the previously reported SOTA by 20%. We demonstrate that this value depends on the dataset and can be even higher.https://peerj.com/articles/cs-1241.pdfSymbolic regressionVAELSTMConstrained optimizationGenerationMachine learning |
| spellingShingle | Sergei Popov Mikhail Lazarev Vladislav Belavin Denis Derkach Andrey Ustyuzhanin Symbolic expression generation via variational auto-encoder PeerJ Computer Science Symbolic regression VAE LSTM Constrained optimization Generation Machine learning |
| title | Symbolic expression generation via variational auto-encoder |
| title_full | Symbolic expression generation via variational auto-encoder |
| title_fullStr | Symbolic expression generation via variational auto-encoder |
| title_full_unstemmed | Symbolic expression generation via variational auto-encoder |
| title_short | Symbolic expression generation via variational auto-encoder |
| title_sort | symbolic expression generation via variational auto encoder |
| topic | Symbolic regression VAE LSTM Constrained optimization Generation Machine learning |
| url | https://peerj.com/articles/cs-1241.pdf |
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