# Goodness of fit by Neyman-Pearson testing

arXiv: https://arxiv.org/abs/2305.14137 · HTML: https://mlsanity.com/paper/2305.14137/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 23 May 2023.

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

- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2106.05285/) (2021)
- [Evaluating generative models in high energy physics](https://mlsanity.com/paper/2211.10295/) (2022)
- [Learning new physics efficiently with nonparametric methods](https://mlsanity.com/paper/2204.02317/) (2022)
- [Fast kernel methods for Data Quality Monitoring as a goodness-of-fit test](https://mlsanity.com/paper/2303.05413/) (2023)
- [A goodness-of-fit test based on a recursive product of spacings](https://mlsanity.com/paper/2111.02252/) (2021)

## Built on by (most cited first, 10 of 10)

- [Refereeing the Referees: Evaluating Two-Sample Tests for Validating Generators in Precision Sciences](https://mlsanity.com/paper/2409.16336/) (2024)
- [Multiple testing for signal-agnostic searches of new physics with machine learning](https://mlsanity.com/paper/2408.12296/) (2024)
- [Comparing Generative Models with the New Physics Learning Machine](https://mlsanity.com/paper/2508.02275/) (2025)
- [Learning to Validate Generative Models: a Goodness-of-Fit Approach](https://mlsanity.com/paper/2511.09118/) (2025)
- [Forecasting Generative Amplification](https://mlsanity.com/paper/2509.08048/) (2025)
- [Model-Agnostic Signal Discovery with Machine Learning: Bridging the Gap Between Theory and Practice](https://mlsanity.com/paper/2605.31103/) (2026)
- [AutoSciDACT: Automated Scientific Discovery through Contrastive Embedding and Hypothesis Testing](https://mlsanity.com/paper/2510.21935/) (2025)
- [Regularized f-Divergence Kernel Tests](https://mlsanity.com/paper/2601.19755/) (2026)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [Sparse, self-organizing ensembles of local kernels detect rare statistical anomalies](https://mlsanity.com/paper/2511.03095/) (2025)

## Abstract (arXiv)

The Neyman-Pearson strategy for hypothesis testing can be employed for goodness of fit if the alternative hypothesis is selected from data by exploring a rich parametrised family of models, while controlling the impact of statistical fluctuations. The New Physics Learning Machine (NPLM) methodology has been developed as a concrete implementation of this idea, to target the detection of new physical effects in the context of high energy physics collider experiments. In this paper we conduct a comparison of this approach to goodness of fit with others, in particular with classifier-based strategies that share strong similarities with NPLM. From our comparison, NPLM emerges as the more sensitive test to small departures of the data from the expected distribution and not biased towards detecting specific types of anomalies. These features make it suited for agnostic searches for new physics at collider experiments. Its deployment in other scientific and industrial scenarios should be investigated.