用物理扰动思想改进高维非参数工具变量估计，误差降低99%。
Perturbative methods for non-parametric instrumental variable
- 借鉴物理扰动理论，对核岭回归进行高阶修正
- 当β>0.7时，预测误差比传统方法低99%
- 适合高维、病态的非参数因果推断场景
我们提出一种非参数工具变量（NPIV）估计的扰动方法。受物理扰动理论启发，将标准核岭回归扩展为包含系统性高阶扰动项，显著提升估计精度。谱分析表明，扰动使积分算子不同特征模态间产生耦合，在积分方程病态时尤为有效，而其成因之一是维度灾难。该方法在多种维度环境下表现良好，尤其当维度参数β（由样本数n与维度d定义为n^β = d）较大时。实验显示，一阶扰动修正可使高维病态情形（β > 0.7）下的预测误差相比标准岭回归降低高达99%，且性能优势随维度增加而增强。
原文摘要 · Abstract (English)
We introduce a perturbative approach for nonparametric instrumental variable (NPIV) estimation. By drawing inspiration from perturbation theory in physics, we extend standard kernel ridge methods with systematic higher perturbation order corrections that significantly improve estimation accuracy. Spectrally, the perturbation introduces mixing between different eigenmodes of the expectation integral operator, which becomes especially useful when the integral equation is ill-defined. One source for such ill-definedness can be the curse of dimensionality. Our method performs across various dimensionality regimes, particularly when the dimensionality parameter $β$ which is defined through the number of samples $n$ and dimension $d$ as $n^β= d$, becomes large. Experimental results show that our first-order perturbative corrections can reduce prediction error by up to 99\% in high-dimensional ill-defined cases ($β> 0.7$) compared to standard ridge regression approaches. The performance improvement is maintained across a wide range of dimensions, with the advantage becoming more pronounced as dimensionality increases.
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。