# Minimax optimal testing by classification

arXiv: https://arxiv.org/abs/2306.11085 · HTML: https://mlsanity.com/paper/2306.11085/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2023.

## Built on by (most cited first, 5 of 5)

- [Discriminative Estimation of Total Variation Distance: A Fidelity Auditor for Generative Data](https://mlsanity.com/paper/2405.15337/) (2024)
- [Boosting Statistic Learning with Synthetic Data from Pretrained Large Models](https://mlsanity.com/paper/2505.04992/) (2025)
- [A Distribution Testing Approach to Clustering Distributions](https://mlsanity.com/paper/2512.08376/) (2025)
- [Zero Flux: Flow-Based Comparison of High-Dimensional Discrete Distributions](https://mlsanity.com/paper/2610.01472/) (2026)
- [From Imbalance to Evidence: Deep Nonparametric Testing for Complex Data under Severe Sample Imbalance](https://mlsanity.com/paper/2610.12946/) (2026)

## Abstract (arXiv)

This paper considers an ML inspired approach to hypothesis testing known as classifier/classification-accuracy testing (mathsfCAT). In mathsfCAT, one first trains a classifier by feeding it labeled synthetic samples generated by the null and alternative distributions, which is then used to predict labels of the actual data samples. This method is widely used in practice when the null and alternative are only specified via simulators (as in many scientific experiments). We study goodness-of-fit, two-sample (mathsfTS) and likelihood-free hypothesis testing (mathsfLFHT), and show that mathsfCAT achieves (near-)minimax optimal sample complexity in both the dependence on the total-variation (mathsfTV) separation ε and the probability of error δ in a variety of non-parametric settings, including discrete distributions, d-dimensional distributions with a smooth density, and the Gaussian sequence model. In particular, we close the high probability sample complexity of mathsfLFHT for each class. As another highlight, we recover the minimax optimal complexity of mathsfTS over discrete distributions, which was recently established by Diakonikolas et al. (2021). The corresponding mathsfCAT simply compares empirical frequencies in the first half of the data, and rejects the null when the classification accuracy on the second half is better than random.