# Nonparametric Online Regression while Learning the Metric

arXiv: https://arxiv.org/abs/1705.07853 · HTML: https://mlsanity.com/paper/1705.07853/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2017.

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

- [AdaTask: Adaptive Multitask Online Learning](https://mlsanity.com/paper/2205.15802/) (2022)
- [Mixture Weight Estimation and Model Prediction in Multi-source Multi-target Domain Adaptation](https://mlsanity.com/paper/2309.10736/) (2023)

## Abstract (arXiv)

We study algorithms for online nonparametric regression that learn the directions along which the regression function is smoother. Our algorithm learns the Mahalanobis metric based on the gradient outer product matrix boldsymbolG of the regression function (automatically adapting to the effective rank of this matrix), while simultaneously bounding the regret ---on the same data sequence--- in terms of the spectrum of boldsymbolG. As a preliminary step in our analysis, we extend a nonparametric online learning algorithm by Hazan and Megiddo enabling it to compete against functions whose Lipschitzness is measured with respect to an arbitrary Mahalanobis metric.