Colby Fronk, Jaewoong Yun, Prashant Singh, Linda Petzold
{"title":"贝叶斯多项式神经网络和多项式神经常微分方程。","authors":"Colby Fronk, Jaewoong Yun, Prashant Singh, Linda Petzold","doi":"10.1371/journal.pcbi.1012414","DOIUrl":null,"url":null,"abstract":"<p><p>Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs.</p>","PeriodicalId":20241,"journal":{"name":"PLoS Computational Biology","volume":"20 10","pages":"e1012414"},"PeriodicalIF":3.8000,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11476690/pdf/","citationCount":"0","resultStr":"{\"title\":\"Bayesian polynomial neural networks and polynomial neural ordinary differential equations.\",\"authors\":\"Colby Fronk, Jaewoong Yun, Prashant Singh, Linda Petzold\",\"doi\":\"10.1371/journal.pcbi.1012414\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs.</p>\",\"PeriodicalId\":20241,\"journal\":{\"name\":\"PLoS Computational Biology\",\"volume\":\"20 10\",\"pages\":\"e1012414\"},\"PeriodicalIF\":3.8000,\"publicationDate\":\"2024-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11476690/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"PLoS Computational Biology\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.1371/journal.pcbi.1012414\",\"RegionNum\":2,\"RegionCategory\":\"生物学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/10/1 0:00:00\",\"PubModel\":\"eCollection\",\"JCR\":\"Q1\",\"JCRName\":\"BIOCHEMICAL RESEARCH METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"PLoS Computational Biology","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1371/journal.pcbi.1012414","RegionNum":2,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/10/1 0:00:00","PubModel":"eCollection","JCR":"Q1","JCRName":"BIOCHEMICAL RESEARCH METHODS","Score":null,"Total":0}
Bayesian polynomial neural networks and polynomial neural ordinary differential equations.
Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs.
期刊介绍：
PLOS Computational Biology features works of exceptional significance that further our understanding of living systems at all scales—from molecules and cells, to patient populations and ecosystems—through the application of computational methods. Readers include life and computational scientists, who can take the important findings presented here to the next level of discovery.
Research articles must be declared as belonging to a relevant section. More information about the sections can be found in the submission guidelines.
Research articles should model aspects of biological systems, demonstrate both methodological and scientific novelty, and provide profound new biological insights.
Generally, reliability and significance of biological discovery through computation should be validated and enriched by experimental studies. Inclusion of experimental validation is not required for publication, but should be referenced where possible. Inclusion of experimental validation of a modest biological discovery through computation does not render a manuscript suitable for PLOS Computational Biology.
Research articles specifically designated as Methods papers should describe outstanding methods of exceptional importance that have been shown, or have the promise to provide new biological insights. The method must already be widely adopted, or have the promise of wide adoption by a broad community of users. Enhancements to existing published methods will only be considered if those enhancements bring exceptional new capabilities.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
