Title: A Perturbative Framework for Non-Parametric Instrumental Variable Estimation

Abstract:

This study presents a novel perturbative strategy for estimating non-parametric instrumental variables (NPIV). Inspired by perturbation theory from physics, we augment conventional kernel ridge regression techniques with systematic higher-order perturbation corrections, a modification that substantially enhances estimation precision. From a spectral perspective, this perturbative framework induces a mixing of the various eigenmodes associated with the expectation integral operator. This mixing effect proves particularly advantageous when dealing with ill-posed integral equations, a scenario often exacerbated by the curse of dimensionality.

Our proposed method demonstrates robust performance across diverse dimensional landscapes, especially in regimes where the dimensionality parameter $\beta$ is high. This parameter is defined by the relationship $n^\beta = d$, linking the number of samples ($n$) to the dimension ($d$). Empirical evaluations indicate that applying first-order perturbative corrections can slash prediction errors by as much as 99% in high-dimensional, ill-defined contexts (specifically where $\beta > 0.7$) when compared to traditional ridge regression methods. These gains are consistent across a broad spectrum of dimensions, with the performance benefits becoming increasingly significant as dimensionality rises.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC