用物理力学原理优化数据拟合，无需调参且抗噪性强。
A kinetic-based regularization method for data science applications
- 借鉴统计力学思想，通过约束数据分布低阶矩来正则化函数学习
- 在高维空间中提升插值与回归精度，尤其适合含噪数据
- 局部计算特性使效率高于径向基函数，适合大规模数据
我们提出一种基于物理学的函数学习正则化技术，受统计力学启发。通过将插值器参数优化类比为系统能量最小化，引入对数据分布低阶矩的约束修正，减少离散与连续表示间的差异，从而进入更优的能量景观，提升插值器精度。该方法在插值和回归任务中表现优异，即使在高维空间亦有效。不同于传统方法，无需经验调参，特别适用于噪声数据。此外，因其局部性质，相比径向基函数插值器，在计算与内存效率上更具优势，尤其适合大规模数据集。
原文摘要 · Abstract (English)
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce corrections that impose constraints on the lower-order moments of the data distribution. This minimizes the discrepancy between the discrete and continuum representations of the data, in turn allowing to access more favorable energy landscapes, thus improving the accuracy of the interpolator. Our approach improves performance in both interpolation and regression tasks, even in high-dimensional spaces. Unlike traditional methods, it does not require empirical parameter tuning, making it particularly effective for handling noisy data. We also show that thanks to its local nature, the method offers computational and memory efficiency advantages over Radial Basis Function interpolators, especially for large datasets.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。