# Semi-Parametric Uncertainty Bounds for Binary Classification

## TL;DR

This paper develops kernel-based semi-parametric methods to construct non-asymptotic confidence regions for the binary classification regression function, ensuring exact coverage and strong consistency.

## Contribution

It introduces three novel resampling methods that provide guaranteed coverage probabilities for the regression function in binary classification.

## Key findings

- All methods guarantee exact coverage probabilities.
- The methods are strongly consistent.
- They improve uncertainty quantification in binary classification.

## Abstract

The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal classifier, moreover, besides providing optimal predictions, it can also assess the risk of misclassification. We aim at building non-asymptotic confidence regions for the regression function and suggest three kernel-based semi-parametric resampling methods. We prove that all of them guarantee regions with exact coverage probabilities and they are strongly consistent.