# Perturbative methods for non-parametric instrumental variable

arXiv: https://arxiv.org/abs/2606.00322 · HTML: https://mlsanity.com/paper/2606.00322/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 11 of 11)

- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [How rotational invariance of common kernels prevents generalization in high dimensions](https://mlsanity.com/paper/2104.04244/) (2021)
- [Spectral Regularized Kernel Two-Sample Tests](https://mlsanity.com/paper/2212.09201/) (2022)
- [(De)-regularized Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/2409.14980/) (2024)
- [Optimal Learning with Anisotropic Gaussian SVMs](https://mlsanity.com/paper/1810.02321/) (2018)
- [Demystifying Spectral Feature Learning for Instrumental Variable Regression](https://mlsanity.com/paper/2506.10899/) (2025)
- [Optimality and Adaptivity of Deep Neural Features for Instrumental Variable Regression](https://mlsanity.com/paper/2501.04898/) (2025)

## Abstract (arXiv)

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 nβ = 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.