动态系统识别,模型选择和模型不确定性量化通过贝叶斯推理
Robert K Niven1, Laurent Cordier2, Ali Mohammad-Djafari3
1School of Engineering and Technology, The University of New South Wales, Canberra, ACT 2600, Australia.
Chaos (Woodbury, N.Y.)
|August 27, 2024
概括
本研究引入了贝叶斯框架,用于从时间序列数据中识别动态系统. 这种方法提供了可靠的模型选择和不确定性量化,优于传统的稀疏回归方法.
科学领域:
- 动态系统理论 动态系统理论
- 统计推理 统计推理
- 机器学习 机器学习
背景情况:
- 时间序列数据分析对于理解复杂系统至关重要.
- 动态系统识别的传统方法往往缺乏强大的不确定性量化.
- 稀疏回归技术提供模型解释性,但可能与复杂的噪声模型作斗争.
研究的目的:
- 为动态系统识别提供贝叶斯最大后期 (MAP) 框架.
- 为系统识别中的规范化术语提供理论上的理由.
- 将贝叶斯算法与现有的稀疏回归方法进行比较.
主要方法:
- 开发了一个贝叶斯式MAP框架,用于动态系统识别.
- 将框架等同于通用的提霍诺夫规范化.
- 采用了联合MAP和变量贝叶斯近似算法.
- 与LASSO,回归和SINDy算法进行性能比较.
主要成果:
- 贝叶斯框架为剩余和规范化术语提供了一个合理的基础.
- 贝叶斯推理允许模型排名,不确定性量化和超参数估计.
- 后部高斯规范是定量模型选择的强有力的指标.
- 贝叶斯方法在识别各种噪音类型的动态系统方面表现出卓越的表现.
结论:
- 拟议的贝叶斯 MAP 框架为动态系统识别提供了一个原则性的方法.
- 与现有方法相比,它为模型选择和不确定性量化提供了增强的能力.
- 该框架对于具有高斯式或拉普拉斯式噪声的系统特别有效.
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