# Exact Distribution-Free Hypothesis Tests for the Regression Function of Binary Classification via Conditional Kernel Mean Embeddings

arXiv: https://arxiv.org/abs/2103.05126 · HTML: https://mlsanity.com/paper/2103.05126/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 8 Mar 2021.

## Builds on (most cited first, 6 of 6)

- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Distribution-free binary classification: prediction sets, confidence intervals and calibration](https://mlsanity.com/paper/2006.10564/) (2020)
- [Characteristic and Universal Tensor Product Kernels](https://mlsanity.com/paper/1708.08157/) (2017)
- [Semi-Parametric Uncertainty Bounds for Binary Classification](https://mlsanity.com/paper/1903.09790/) (2019)
- [Regularised Least-Squares Regression with Infinite-Dimensional Output Space](https://mlsanity.com/paper/2010.10973/) (2020)

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

- [T-Cal: An optimal test for the calibration of predictive models](https://mlsanity.com/paper/2203.01850/) (2022)
- [Sample Complexity of the Sign-Perturbed Sums Identification Method: Scalar Case](https://mlsanity.com/paper/2401.15792/) (2024)
- [Recursive Estimation of Conditional Kernel Mean Embeddings](https://mlsanity.com/paper/2302.05955/) (2023)
- [Resampled Confidence Regions with Exponential Shrinkage for the Regression Function of Binary Classification](https://mlsanity.com/paper/2308.01835/) (2023)

## Abstract (arXiv)

In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines both the Bayes optimal classifier and the misclassification probabilities. A resampling based framework is presented and combined with consistent point estimators of the conditional kernel mean map, in order to construct distribution-free hypothesis tests. These tests are introduced in a flexible manner allowing us to control the exact probability of type I error for any sample size. We also prove that both proposed techniques are consistent under weak statistical assumptions, i.e., the type II error probabilities pointwise converge to zero.