# Non-parametric Binary regression in metric spaces with KL loss

arXiv: https://arxiv.org/abs/2010.09886 · HTML: https://mlsanity.com/paper/2010.09886/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [Capturing Individual Human Preferences with Reward Features](https://mlsanity.com/paper/2503.17338/) (2025)

## Abstract (arXiv)

We propose a non-parametric variant of binary regression, where the hypothesis is regularized to be a Lipschitz function taking a metric space to [0,1] and the loss is logarithmic. This setting presents novel computational and statistical challenges. On the computational front, we derive a novel efficient optimization algorithm based on interior point methods; an attractive feature is that it is parameter-free (i.e., does not require tuning an update step size). On the statistical front, the unbounded loss function presents a problem for classic generalization bounds, based on covering-number and Rademacher techniques. We get around this challenge via an adaptive truncation approach, and also present a lower bound indicating that the truncation is, in some sense, necessary.