# Classification without labels: Learning from mixed samples in high energy physics

arXiv: https://arxiv.org/abs/1708.02949 · HTML: https://mlsanity.com/paper/1708.02949/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2017.

## Built on by (most cited first, 30 of 43)

- [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)
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- [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)
- [Is Tokenization Needed for Masked Particle Modelling?](https://mlsanity.com/paper/2409.12589/) (2024)
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- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once](https://mlsanity.com/paper/2101.07263/) (2021)
- [Comparing Weak- and Unsupervised Methods for Resonant Anomaly Detection](https://mlsanity.com/paper/2104.02092/) (2021)
- [High-dimensional and Permutation Invariant Anomaly Detection](https://mlsanity.com/paper/2306.03933/) (2023)
- [Anomalies, Representations, and Self-Supervision](https://mlsanity.com/paper/2301.04660/) (2023)
- [Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learning](https://mlsanity.com/paper/2209.07559/) (2022)
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- [Improving new physics searches with diffusion models for event observables and jet constituents](https://mlsanity.com/paper/2312.10130/) (2023)
- [Neural Embedding: Learning the Embedding of the Manifold of Physics Data](https://mlsanity.com/paper/2208.05484/) (2022)
- [New Methods and Datasets for Group Anomaly Detection From Fundamental Physics](https://mlsanity.com/paper/2107.02821/) (2021)
- [Optimal Equivariant Architectures from the Symmetries of Matrix-Element Likelihoods](https://mlsanity.com/paper/2410.18553/) (2024)
- [Resonant Anomaly Detection with Multiple Reference Datasets](https://mlsanity.com/paper/2212.10579/) (2022)
- [Machine-Learned Exclusion Limits without Binning](https://mlsanity.com/paper/2211.04806/) (2022)
- [Agents of Discovery](https://mlsanity.com/paper/2509.08535/) (2025)
- [Model-Agnostic Signal Discovery with Machine Learning: Bridging the Gap Between Theory and Practice](https://mlsanity.com/paper/2605.31103/) (2026)
- [Improving the performance of weak supervision searches using transfer and meta-learning](https://mlsanity.com/paper/2312.06152/) (2023)
- [Neural Quasiprobabilistic Likelihood Ratio Estimation with Negatively Weighted Data](https://mlsanity.com/paper/2410.10216/) (2024)
- [AutoSciDACT: Automated Scientific Discovery through Contrastive Embedding and Hypothesis Testing](https://mlsanity.com/paper/2510.21935/) (2025)
- [Towards a method to anticipate dark matter signals with deep learning at the LHC](https://mlsanity.com/paper/2105.12018/) (2021)
- [Interpretable Boosted Decision Tree Analysis for the Majorana Demonstrator](https://mlsanity.com/paper/2207.10710/) (2022)
- [Weakly-Supervised Anomaly Detection in the Milky Way](https://mlsanity.com/paper/2305.03761/) (2023)
- [Triggering Dark Showers with Conditional Dual Auto-Encoders](https://mlsanity.com/paper/2306.12955/) (2023)

## Abstract (arXiv)

Modern machine learning techniques can be used to construct powerful models for difficult collider physics problems. In many applications, however, these models are trained on imperfect simulations due to a lack of truth-level information in the data, which risks the model learning artifacts of the simulation. In this paper, we introduce the paradigm of classification without labels (CWoLa) in which a classifier is trained to distinguish statistical mixtures of classes, which are common in collider physics. Crucially, neither individual labels nor class proportions are required, yet we prove that the optimal classifier in the CWoLa paradigm is also the optimal classifier in the traditional fully-supervised case where all label information is available. After demonstrating the power of this method in an analytical toy example, we consider a realistic benchmark for collider physics: distinguishing quark- versus gluon-initiated jets using mixed quark/gluon training samples. More generally, CWoLa can be applied to any classification problem where labels or class proportions are unknown or simulations are unreliable, but statistical mixtures of the classes are available.