用概率方法实现自动方程发现，更可靠且有理论保证
Bayesian symbolic regression: Automated equation discovery from a physicists' perspective
- 基于概率框架构建模型，避免传统启发式方法
- 可评估模型合理性并提供性能保障
- 推荐物理学者与需要可解释模型的研究者阅读
符号回归能从数据中自动学习闭合形式的数学模型。传统符号回归及新兴深度学习方法依赖启发式模型选择、正则化和模型空间探索。本文提出概率方法，与信息论和统计物理直接关联，从基本假设和显式近似出发，建立模型合理性判断，并提供启发式方法所缺乏的性能保证。该方法还促使我们考虑模型集成而非单一模型，提升可靠性与泛化能力。
原文摘要 · Abstract (English)
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic regularization, and heuristic exploration of model space. Here, we discuss the probabilistic approach to symbolic regression, an alternative to such heuristic approaches with direct connections to information theory and statistical physics. We show how the probabilistic approach establishes model plausibility from basic considerations and explicit approximations, and how it provides guarantees of performance that heuristic approaches lack. We also discuss how the probabilistic approach compels us to consider model ensembles, as opposed to single models.
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