重新审视切比雪夫多项式和各向异性RBF模型在表格回归中的应用
Revisiting Chebyshev Polynomial and Anisotropic RBF Models for Tabular Regression
AI总结：
本文在55个数据集上基准测试切比雪夫多项式回归器、各向异性RBF网络和平滑树混合模型，发现平滑模型在CPU可行模型中与树集成准确率相当且泛化差距更小，建议将其纳入候选池。
摘要：
平滑基模型如切比雪夫多项式回归器和径向基函数（RBF）网络在数值分析中已得到充分确立。它们的连续可微预测表面适用于代理优化、敏感性分析以及其他响应随输入逐渐变化的环境。尽管具有这些特性，平滑模型在树集成主导的表格回归中很少出现。我们探究它们是否能够竞争，跨55个按应用领域组织的回归数据集对模型进行基准测试。我们开发了一种各向异性RBF网络，具有数据驱动的中心放置和基于梯度的宽度优化，一个岭正则化的切比雪夫多项式回归器，以及一个平滑树混合模型（切比雪夫模型树）；这三个模型均作为scikit-learn兼容包发布。我们将这些模型与树集成、预训练transformer和标准基线进行基准测试，评估准确性和泛化行为。transformer在大多数数据集上准确率排名第一，但其GPU依赖性、推理延迟和数据集大小限制制约了其在应用科学和工业中常见的基于CPU环境中的部署。在CPU可行的模型中，平滑模型和树集成在准确率上统计上持平，但前者倾向于表现出更紧的泛化差距。我们建议常规地将平滑基模型纳入候选池，特别是当下游使用受益于更紧的泛化和逐渐变化的预测时。
英文摘要：
Smooth-basis models such as Chebyshev polynomial regressors and radial basis function (RBF) networks are well established in numerical analysis. Their continuously differentiable prediction surfaces suit surrogate optimisation, sensitivity analysis, and other settings where the response varies gradually with inputs. Despite these properties, smooth models seldom appear in tabular regression, where tree ensembles dominate. We ask whether they can compete, benchmarking models across 55 regression datasets organised by application domain. We develop an anisotropic RBF network with data-driven centre placement and gradient-based width optimisation, a ridge-regularised Chebyshev polynomial regressor, and a smooth-tree hybrid (Chebyshev model tree); all three are released as scikit-learn-compatible packages. We benchmark these against tree ensembles, a pre-trained transformer, and standard baselines, evaluating accuracy alongside generalisation behaviour. The transformer ranks first on accuracy across a majority of datasets, but its GPU dependence, inference latency, and dataset-size limits constrain deployment in the CPU-based settings common across applied science and industry. Among CPU-viable models, smooth models and tree ensembles are statistically tied on accuracy, but the former tend to exhibit tighter generalisation gaps. We recommend routinely including smooth-basis models in the candidate pool, particularly when downstream use benefits from tighter generalisation and gradually varying predictions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
