SyMANTIC：一种用于科学及其他领域可解释且简约模型发现的高效符号回归方法
SyMANTIC: An Efficient Symbolic Regression Method for Interpretable and Parsimonious Model Discovery in Science and Beyond
AI总结：
SyMANTIC通过互信息特征选择、自适应特征扩展和递归稀疏回归高效发现低维可解释数学表达式，以远低于现有符号回归方法的成本获得相似或更准确的模型。
摘要：
符号回归（SR）是机器学习的一个新兴分支，专注于从数据中发现简单且可解释的数学表达式。尽管已经开发了各种各样的SR方法，但它们常常面临诸如高计算成本、对输入维度数量的可扩展性差、对噪声的脆弱性以及无法平衡准确性与复杂度等挑战。本文介绍了SyMANTIC，一种解决这些挑战的新型SR算法。SyMANTIC通过基于互信息的特征选择、自适应特征扩展和递归应用的基于$\ell_0$的稀疏回归的独特组合，从大量候选特征（从约$10^5$到约$10^{10}$或更多）中高效地识别（可能是多个）低维描述符。此外，它采用信息论度量来产生一组近似的帕累托最优方程，每个方程在给定复杂度下提供最佳发现的准确性。此外，我们基于PyTorch生态系统构建的SyMANTIC开源实现便于安装和GPU加速。我们在一系列问题上展示了SyMANTIC的有效性，包括合成示例、科学基准、真实世界的材料性质预测以及从小数据集进行混沌动力系统识别。大量比较表明，SyMANTIC以现有SR方法成本的一小部分发现了相似或更准确的模型。
英文摘要：
Symbolic regression (SR) is an emerging branch of machine learning focused on discovering simple and interpretable mathematical expressions from data. Although a wide-variety of SR methods have been developed, they often face challenges such as high computational cost, poor scalability with respect to the number of input dimensions, fragility to noise, and an inability to balance accuracy and complexity. This work introduces SyMANTIC, a novel SR algorithm that addresses these challenges. SyMANTIC efficiently identifies (potentially several) low-dimensional descriptors from a large set of candidates (from $\sim 10^5$ to $\sim 10^{10}$ or more) through a unique combination of mutual information-based feature selection, adaptive feature expansion, and recursively applied $\ell_0$-based sparse regression. In addition, it employs an information-theoretic measure to produce an approximate set of Pareto-optimal equations, each offering the best-found accuracy for a given complexity. Furthermore, our open-source implementation of SyMANTIC, built on the PyTorch ecosystem, facilitates easy installation and GPU acceleration. We demonstrate the effectiveness of SyMANTIC across a range of problems, including synthetic examples, scientific benchmarks, real-world material property predictions, and chaotic dynamical system identification from small datasets. Extensive comparisons show that SyMANTIC uncovers similar or more accurate models at a fraction of the cost of existing SR methods.
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