提出可分离性建模方法，解决交互项导致的解释失真问题
Beyond Additive Decompositions: Interpretability Through Separability
- 用分阶段贪婪算法学习特征函数的秩1乘积之和，强制模型可分离
- 在回归基准上性能媲美黑盒模型，且能还原出一阶部分依赖函数
- 适合需要高保真可视化解释的复杂模型场景
可解释机器学习要求模型既准确又结构上忠实于数据。现有解释方法多依赖加性表示（如广义加性模型、SHAP、函数型方差分析），在强交互存在时易出现信号抵消和支撑外外推问题。本文提出张量分离学习（TSL），一种通过分阶段贪婪过程与正交重拟合学习特征函数秩-1乘积之和的回归模型。通过强制可分离性，TSL避免了因边际化高阶交互而造成的信息损失。所学的TSL模型可完全由一阶部分依赖函数重构（至常数因子），阶段对应关系确保可视化结果忠实于拟合成分。我们建立了具有有界混合p阶偏导数函数的逼近率保证，并证明TSL在回归基准上可与黑盒模型竞争。
原文摘要 · Abstract (English)
Interpretable machine learning requires models that are accurate and structurally faithful to the data. Existing explainability methods rely heavily on additive representations (e.g., Generalized Additive Models (GAMs), SHapley Additive exPlanations (SHAP), functional ANOVA), which can suffer from signal cancellation and off-support extrapolation in the presence of strong interactions. We propose Tensor Separation Learning (TSL), a regression model that learns a sum of rank-1 products of univariate per-feature functions via a stagewise greedy procedure with orthogonal refitting. By enforcing separability, TSL avoids the information loss inherent in additive projections caused by marginalizing higher-order interactions. The learned TSL model can be fully reconstructed from first-order partial dependence functions, up to constant factors. This stage-wise correspondence ensures that the resulting visualizations are faithful to the fitted components. We establish approximation-rate guarantees for functions with bounded mixed $p$-th order partial derivatives and demonstrate that TSL competes with black-box models on regression benchmarks.
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