# Kernel regression, minimax rates and effective dimensionality: beyond the regular case

arXiv: https://arxiv.org/abs/1611.03979 · HTML: https://mlsanity.com/paper/1611.03979/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2016.

## Built on by (most cited first, 4 of 4)

- [Optimal Learning Rates for Regularized Least-Squares with a Fourier Capacity Condition](https://mlsanity.com/paper/2204.07856/) (2022)
- [Forecasting time series with constraints](https://mlsanity.com/paper/2502.10485/) (2025)
- [Minimax Rates and Spectral Distillation for Tree Ensembles](https://mlsanity.com/paper/2605.11841/) (2026)
- [Statistical inverse learning and ℓ1-regularization](https://mlsanity.com/paper/2607.07468/) (2026)

## Abstract (arXiv)

We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kernel mapping covariance operator. In the perspective of distribution-free results, we investigate this issue under much weaker assumption on the eigenvalue decay, allowing for more complex behavior that can reflect different structure of the data at different scales.