# Learning to Classify from Impure Samples with High-Dimensional Data

arXiv: https://arxiv.org/abs/1801.10158 · HTML: https://mlsanity.com/paper/1801.10158/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2018.

## 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)
- [Autoencoders for unsupervised anomaly detection in high energy physics](https://mlsanity.com/paper/2104.09051/) (2021)
- [The Dark Machines Anomaly Score Challenge: Benchmark Data and Model Independent Event Classification for the Large Hadron Collider](https://mlsanity.com/paper/2105.14027/) (2021)
- [Challenges for Unsupervised Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2110.06948/) (2021)
- [Machine learning on small size samples: A synthetic knowledge synthesis](https://mlsanity.com/paper/2103.01002/) (2021)
- [Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learning](https://mlsanity.com/paper/2209.07559/) (2022)
- [Multiclass Classification without Labels via Posterior Simplex Geometry](https://mlsanity.com/paper/2607.24943/) (2026)

## Abstract (arXiv)

A persistent challenge in practical classification tasks is that labeled training sets are not always available. In particle physics, this challenge is surmounted by the use of simulations. These simulations accurately reproduce most features of data, but cannot be trusted to capture all of the complex correlations exploitable by modern machine learning methods. Recent work in weakly supervised learning has shown that simple, low-dimensional classifiers can be trained using only the impure mixtures present in data. Here, we demonstrate that complex, high-dimensional classifiers can also be trained on impure mixtures using weak supervision techniques, with performance comparable to what could be achieved with pure samples. Using weak supervision will therefore allow us to avoid relying exclusively on simulations for high-dimensional classification. This work opens the door to a new regime whereby complex models are trained directly on data, providing direct access to probe the underlying physics.