DeepPySR提升科学发现中的符号回归效率与可解释性。
DeepPySR -- A Symbolic Regression Framework with Dynamic Pruning, Pareto Selection, and Hierarchical Composition for Real-World Scientific Discovery
- 动态剪枝+分层组合，自动筛选关键变量并构建复杂公式
- 在多个真实数据集上显著超越基线，最高提升13.6%的预测精度
- 适合需要透明模型的医学、社会科学等高可信场景
符号回归（SR）从数据中发现解析方程，生成可直接解释的白盒模型，优于依赖不稳定后处理工具的黑箱方法。在临床医学与社会科学研究中，这种透明性至关重要，但SR面临三大挑战：高维输入、帕累托前沿公式的合理选择，以及多重共线性、类别不平衡等数据不规则问题。本文提出DeepPySR，通过动态变量剪枝策略在搜索过程中剔除无关特征，采用指数型帕累托选择准则消除准确率与复杂度间的权衡，并设计多层架构实现分层符号组合。在四个费曼物理基准和七个生物医学与社会科学数据集上，DeepPySR表现优异：体脂预测R²达0.794（基线0.702），心脏病预测F1达0.898（基线0.787），学生成绩预测R²达0.964（基线0.948），雷恩BMI预测R²达0.525（基线0.370），且生成的公式与领域风险因素一致。
原文摘要 · Abstract (English)
Symbolic regression (SR) discovers analytical equations from data, yielding glass-box models with directly interpretable formulas, unlike black-box methods that rely on unstable post-hoc tools such as SHAP or LIME. This transparency is crucial in clinical medicine and social science, but SR faces three challenges: high-dimensional inputs, principled selection of Pareto-front formulae, and data irregularities such as multicollinearity and class imbalance. We introduce DeepPySR, which addresses these issues with a dynamic variable-pruning schedule to remove irrelevant features during search, an exponential Pareto selection criterion that eliminates trade-offs between accuracy and complexity, and a multi-layer architecture for hierarchical symbolic composition. On four Feynman physics benchmarks and seven biomedical and social-science datasets, DeepPySR outperforms PySR and baselines on body fat (R$^2$: 0.794 vs.\ 0.702), heart disease (F1: 0.898 vs.\ 0.787), student performance (R$^2$: 0.964 vs.\ 0.948), and Raine BMI (R$^2$: 0.525 vs.\ 0.370), producing interpretable formulas aligned with domain risk factors.
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