# Optimal statistical inference in the presence of systematic uncertainties using neural network optimization based on binned Poisson likelihoods with nuisance parameters

arXiv: https://arxiv.org/abs/2003.07186 · HTML: https://mlsanity.com/paper/2003.07186/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2020.

## Built on by (most cited first, 8 of 8)

- [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)
- [A Cautionary Tale of Decorrelating Theory Uncertainties](https://mlsanity.com/paper/2109.08159/) (2021)
- [Bias and Priors in Machine Learning Calibrations for High Energy Physics](https://mlsanity.com/paper/2205.05084/) (2022)
- [FAIR Universe HiggsML Uncertainty Dataset and Competition](https://mlsanity.com/paper/2410.02867/) (2024)
- [Designing Observables for Measurements with Deep Learning](https://mlsanity.com/paper/2310.08717/) (2023)
- [Learning to bin: differentiable and Bayesian optimization for multi-dimensional discriminants in high-energy physics](https://mlsanity.com/paper/2601.07756/) (2026)
- [Hybrid Neural Simulation-Based Inference for Robust Applications and Limited-Budget Scenarios](https://mlsanity.com/paper/2609.36044/) (2026)

## Abstract (arXiv)

Data analysis in science, e.g., high-energy particle physics, is often subject to an intractable likelihood if the observables and observations span a high-dimensional input space. Typically the problem is solved by reducing the dimensionality using feature engineering and histograms, whereby the latter technique allows to build the likelihood using Poisson statistics. However, in the presence of systematic uncertainties represented by nuisance parameters in the likelihood, the optimal dimensionality reduction with a minimal loss of information about the parameters of interest is not known. This work presents a novel strategy to construct the dimensionality reduction with neural networks for feature engineering and a differential formulation of histograms so that the full workflow can be optimized with the result of the statistical inference, e.g., the variance of a parameter of interest, as objective. We discuss how this approach results in an estimate of the parameters of interest that is close to optimal and the applicability of the technique is demonstrated with a simple example based on pseudo-experiments and a more complex example from high-energy particle physics.