arXiv:2608.09162cs.LGcs.AI2026-08

通过优化目标函数平滑性,提升表格数据数值特征的可学习性。

Tabular Numeric Stretch Transformation

论文配图:Tabular Numeric Stretch Transformation
图 1 · 摘自论文原文
  • 将数值特征预处理建模为优化问题,使目标函数更平滑。
  • 在38个数据集上,监督式拉伸法优于所有基线方法。
  • 适合关注表格数据深度学习性能提升的研究者。

表格数据因数值特征分布、尺度和统计特性差异大,给深度学习带来独特挑战。尽管近期进展提升了模型对表格数据的学习能力,但数值特征如何转化为模型友好表示仍研究不足。本文提出拉伸变换框架,将数值特征预处理视为优化问题,以提升目标函数的平滑性,从而增强可学习性。该框架包含两种变体:(1) 无监督拉伸,通过极小极大优化统一重分布特征密度;(2) 监督拉伸,从目标函数平滑性角度,最小化变换空间中的目标函数狄利克雷能量。理论分析表明,无监督拉伸与分段线性编码具有共享分段线性几何结构,且随箱数增加趋近经验累积分布函数变换;监督拉伸在细箱极限下接近目标编码。在TALENT基准的38个数据集上进行的全面实验表明,监督拉伸持续优于所有基线方法。结果表明,显式优化目标函数平滑性是表格深度学习中强大而未被充分探索的策略。

原文摘要 · Abstract (English)

Tabular data presents unique challenges for deep learning due to its heterogeneous nature, where numeric features exhibit diverse distributions, scales, and statistical properties. Although recent advances have improved how models learn from tabular data, how numeric data are transformed into model-friendly representations remains comparatively underexplored. We introduce the stretch transformation framework, which formulates numeric feature preprocessing as an optimization problem to make the target function smoother and thus more learnable. Our framework has two variants: (1) unsupervised stretch, which uniformly redistributes feature density via minimax optimization, and (2) supervised stretch, which optimizes target-aware numeric feature transformations from the perspective of target-function smoothness by minimizing the target function's Dirichlet energy in the transformed space. Our theoretical analysis further connects this framework to several popular transformations: unsupervised stretch is closely related to Piecewise Linear Encoding through a shared piecewise-linear geometry and approaches the empirical CDF transformation as the number of bins grows, while supervised stretch becomes closely related to target encoding in the fine-binning limit. Comprehensive experiments on 38 datasets from the TALENT benchmark demonstrate that supervised stretch consistently outperforms all baselines. These results show that explicitly optimizing for target function smoothness is a powerful and underexplored strategy for tabular deep learning.

表格数据特征变换深度学习优化

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