# Machine-Learned Exclusion Limits without Binning

arXiv: https://arxiv.org/abs/2211.04806 · HTML: https://mlsanity.com/paper/2211.04806/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 64 references that are in the map.
- First posted on arXiv 9 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [Machine Learning in High Energy Physics Community White Paper](https://mlsanity.com/paper/1807.02876/) (2018)
- [Classification without labels: Learning from mixed samples in high energy physics](https://mlsanity.com/paper/1708.02949/) (2017)
- [Neural Density Estimation and Likelihood-free Inference](https://mlsanity.com/paper/1910.13233/) (2019)
- [Learning new physics efficiently with nonparametric methods](https://mlsanity.com/paper/2204.02317/) (2022)
- [E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once](https://mlsanity.com/paper/2101.07263/) (2021)
- [Online-compatible Unsupervised Non-resonant Anomaly Detection](https://mlsanity.com/paper/2111.06417/) (2021)
- [Towards a method to anticipate dark matter signals with deep learning at the LHC](https://mlsanity.com/paper/2105.12018/) (2021)

## Built on by (most cited first, 3 of 3)

- [Machine-Learning Analysis of Radiative Decays to Dark Matter at the LHC](https://mlsanity.com/paper/2410.13799/) (2024)
- [BitHEP -- The Limits of Low-Precision ML in HEP](https://mlsanity.com/paper/2504.03387/) (2025)
- [Shedding Light on Dark Matter at the LHC with Machine Learning](https://mlsanity.com/paper/2509.15121/) (2025)

## Abstract (arXiv)

Machine-Learned Likelihoods (MLL) combines machine-learning classification techniques with likelihood-based inference tests to estimate the experimental sensitivity of high-dimensional data sets. We extend the MLL method by including Kernel Density Estimators (KDE) to avoid binning the classifier output to extract the resulting one-dimensional signal and background probability density functions. We first test our method on toy models generated with multivariate Gaussian distributions, where the true probability distribution functions are known. Later, we apply the method to two cases of interest at the LHC: a search for exotic Higgs bosons, and a Z' boson decaying into lepton pairs. In contrast to physical-based quantities, the typical fluctuations of the ML outputs give non-smooth probability distributions for pure-signal and pure-background samples. The non-smoothness is propagated into the density estimation due to the good performance and flexibility of the KDE method. We study its impact on the final significance computation, and we compare the results using the average of several independent ML output realizations, which allows us to obtain smoother distributions. We conclude that the significance estimation turns out to be not sensible to this issue.