# Kernel Ridge Regression Inference

arXiv: https://arxiv.org/abs/2302.06578 · HTML: https://mlsanity.com/paper/2302.06578/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2023.

## Built on by (most cited first, 6 of 6)

- [Beyond Real Data: Synthetic Data through the Lens of Regularization](https://mlsanity.com/paper/2510.08095/) (2025)
- [Optimal Confidence Band for Kernel Gradient Flow Estimator](https://mlsanity.com/paper/2605.05768/) (2026)
- [Kernel conditional tests from learning-theoretic bounds](https://mlsanity.com/paper/2506.03898/) (2025)
- [Differentiable Kernel Ridge Regression for Deep Learning Pipelines](https://mlsanity.com/paper/2605.02313/) (2026)
- [Nonparametric Goodness-of-fit Testing under Covariate Shift](https://mlsanity.com/paper/2608.04860/) (2026)
- [Calibrated Derivative-Process Sensitivity for Gaussian-Process Variable Selection](https://mlsanity.com/paper/2609.33549/) (2026)

## Abstract (arXiv)

We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student preferences in school matching mechanisms--the inferential theory of KRR is not fully known. We construct valid and sharp confidence sets that shrink at nearly the minimax rate, allowing nonstandard regressors. Our bootstrap procedure uses anti-symmetric multipliers for computational efficiency and for validity under mis-specification. We use the procedure to develop a test for match effects, i.e. whether students benefit more from the schools they rank highly.