# Regularised Least-Squares Regression with Infinite-Dimensional Output Space

arXiv: https://arxiv.org/abs/2010.10973 · HTML: https://mlsanity.com/paper/2010.10973/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2020.

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

- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes](https://mlsanity.com/paper/2109.03582/) (2021)
- [Exact Distribution-Free Hypothesis Tests for the Regression Function of Binary Classification via Conditional Kernel Mean Embeddings](https://mlsanity.com/paper/2103.05126/) (2021)
- [On the Consistency of Kernel Methods with Dependent Observations](https://mlsanity.com/paper/2406.06101/) (2024)

## Abstract (arXiv)

This short technical report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression, where the input space is allowed to be non-compact and the output space is a (possibly infinite-dimensional) Hilbert space. Our approach is based on the integral operator technique using spectral theory for non-compact operators. We place a particular emphasis on obtaining results with as few assumptions as possible; as such we only use Chebyshev's inequality, and no effort is made to obtain the best rates or constants.