# Efficient Kirszbraun Extension with Applications to Regression

arXiv: https://arxiv.org/abs/1905.11930 · HTML: https://mlsanity.com/paper/1905.11930/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2019.

## Built on by (most cited first, 2 of 2)

- [Replicable Clustering](https://mlsanity.com/paper/2302.10359/) (2023)
- [Universal Regression with Adversarial Responses](https://mlsanity.com/paper/2203.05067/) (2022)

## Abstract (arXiv)

We introduce a framework for performing regression between two Hilbert spaces. This is done based on Kirszbraun's extension theorem, to the best of our knowledge, the first application of this technique to supervised learning. We analyze the statistical and computational aspects of this method. We decompose this task into two stages: training (which corresponds operationally to smoothing/regularization) and prediction (which is achieved via Kirszbraun extension). Both are solved algorithmically via a novel multiplicative weight updates (MWU) scheme, which, for our problem formulation, achieves a quadratic runtime improvement over the state of the art. Our empirical results indicate a dramatic improvement over standard off-the-shelf solvers in our setting.