# Neural Quasiprobabilistic Likelihood Ratio Estimation with Negatively Weighted Data

arXiv: https://arxiv.org/abs/2410.10216 · HTML: https://mlsanity.com/paper/2410.10216/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 14 Oct 2024.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Mining gold from implicit models to improve likelihood-free inference](https://mlsanity.com/paper/1805.12244/) (2018)
- [Classification without labels: Learning from mixed samples in high energy physics](https://mlsanity.com/paper/1708.02949/) (2017)
- [A Guide to Constraining Effective Field Theories with Machine Learning](https://mlsanity.com/paper/1805.00020/) (2018)
- [E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once](https://mlsanity.com/paper/2101.07263/) (2021)
- [Improving Generative Model-based Unfolding with Schr"odinger Bridges](https://mlsanity.com/paper/2308.12351/) (2023)
- [Likelihood-free inference with an improved cross-entropy estimator](https://mlsanity.com/paper/1808.00973/) (2018)
- [Machine Learning on data with sPlot background subtraction](https://mlsanity.com/paper/1905.11719/) (2019)

## Built on by (most cited first, 2 of 2)

- [Quasiprobabilistic Density Ratio Estimation with a Reverse Engineered Classification Loss Function](https://mlsanity.com/paper/2512.19913/) (2025)
- [General Flexible f-divergence for Challenging Offline RL Datasets with Low Stochasticity and Diverse Behavior Policies](https://mlsanity.com/paper/2602.11087/) (2026)

## Abstract (arXiv)

Motivated by real-world situations found in high energy particle physics, we consider a generalisation of the likelihood-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. By extension, this framing also applies to importance sampling in a setting where the importance weights can be negative. The presence of negative densities and negative weights, pose an array of challenges to traditional neural likelihood ratio estimation methods. We address these challenges by introducing a novel loss function. In addition, we introduce a new model architecture based on the decomposition of a likelihood ratio using signed mixture models, providing a second strategy for overcoming these challenges. Finally, we demonstrate our approach on a pedagogical example and a real-world example from particle physics.