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Weakly Supervised Classification in High Energy Physics
Lucio Mwinmaarong Dery, Benjamin Nachman, Francesco Rubbo, Ariel Schwartzman
TL;DR
Quark/gluon tagging combines known class fractions with discriminating features that simulations model poorly, while supervised methods often rely on simulated labeled data. The paper trains on unlabeled mixtures using class proportions and reports performance matching fully supervised tagging, with robustness to realistic feature mis-modeling.
Problem
Supervised classifiers often use large simulated labeled datasets, but simulation-optimized methods are not guaranteed optimal in nature, and quark/gluon discriminants are poorly modeled despite known sample fractions.
Source: §1 · p. 2Method
Results
The weakly supervised classifier matches the fully supervised neural network and is robust against a realistic amount of input-variable mis-modeling.
Source: §3 · p. 7Takeaways & Limitations
In quark/gluon and related settings, the approach can train directly on unlabeled data rather than labeled but unreliable simulation, and has broad applicability.
Source: §4 · p. 7The approach requires class-specific feature distributions to remain the same across batches, and its loss leaves classifier-output orientation ambiguous.
Source: §2 · pp. 3, 5
Abstract
from arXiv · showhide
As machine learning algorithms become increasingly sophisticated to exploit subtle features of the data, they often become more dependent on simulations. This paper presents a new approach called weakly supervised classification in which class proportions are the only input into the machine learning algorithm. Using one of the most challenging binary classification tasks in high energy physics - quark versus gluon tagging - we show that weakly supervised classification can match the performance of fully supervised algorithms. Furthermore, by design, the new algorithm is insensitive to any mis-modeling of discriminating features in the data by the simulation. Weakly supervised classification is a general procedure that can be applied to a wide variety of learning problems to boost performance and robustness when detailed simulations are not reliable or not available.
1 Introduction
Sophisticated supervised analyses often depend on simulations, though simulation-optimized methods are not guaranteed to be optimal in nature. The paper introduces training from unlabeled data using class proportions and motivates quark-versus-gluon tagging as an application.
1 Introduction
- Increasingly sophisticated supervised learning combines subtle event features using large simulated labeled datasets, but methods optimized in simulation are not guaranteed to be optimal in nature.Source: §1 · p. 2
- Weakly supervised classification trains on unlabeled data, and here the expected class-A fraction in each bag is known rather than individual instance labels.The paper distinguishes this setup from earlier bag-level supervision, where labels indicated whether a bag contained at least one class-A instance.Source: §1 · p. 2
- Quark/gluon discrimination is a suitable test because class fractions are often known while standard discriminants are poorly modeled by state-of-the-art simulations.The paper uses this task as its main example of weakly supervised classification.Source: §1 · p. 2
- The paper proceeds from the method and its practical application to quark/gluon tagging to concluding remarks; source code is available at DOI 10.5281/zenodo.322813.Source: §1 · p. 2
2 Weakly supervised classification
Weakly supervised classification trains from class proportions rather than individual labels, using multiple batches with different proportions to constrain the classifier. The section explains this approach through a histogram-mixture argument and reports how its performance and stability vary in a toy example.
2 Weakly supervised classification
- Weakly supervised classification minimizes a loss using class proportions instead of individual labels, with multiple batches providing different proportions.The method assumes each class’s feature distribution is the same across batches.Source: §2 · p. 3
- A histogram-mixture argument recovers the class-specific feature distributions from batch histograms, except in contrived cases.Their ratio gives an approximately optimal classifier; the paper says direct bin-by-bin solving is intractable for many dimensions or few examples.Source: §2 · p. 3
- The example’s weakly supervised network uses three inputs, 30 hidden neurons, a sigmoid output, and Adam optimization.It is trained for 25 iterations with a learning rate of 0.009.Source: §2 · p. 4
- The weakly supervised classifier has the same ROC and identical classification performance as the fully supervised classifier in the toy example.The comparison uses three features and nine training subsets with proportions between 0.2 and 0.4.Source: §2 · p. 4, Figure 1 · p. 4
- As the difference between batch proportions increases, median AUC improves and AUC variability decreases across repeated trainings.Figure 2 summarizes 100 trainings per point, with one proportion fixed at 0.2.Source: §2 · p. 5, Figure 2 · p. 5
3 Example: quark and gluon jet discrimination
Quark/gluon tagging is useful because sample-level quark fractions are known while discriminating features are often mis-modeled. In this setting, weakly supervised training matches the fully supervised network and avoids a reported 10% bias under distorted pseudo-data.
3 Example: quark and gluon jet discrimination
- Quark-enriched processes include hadronic W decays, vector-boson-fusion jets, and multiquarks from supersymmetry, despite gluon jets being plentiful at the LHC.The passage notes these as prominent examples of processes yielding mostly quark jets.Source: §3 · p. 5
- Even when proportions differ by only a few percent, stable performance can be achieved if multiple (>2) subsets with different proportions are used for training.The weakly supervised classifier has one hidden layer of size 30 and is trained using 12 bins of the absolute pseudorapidity difference distribution between the two jets.Source: §3 · pp. 5–6
- Quark fractions are known for event samples, while useful discriminating features are often mis-modeled by simulation, motivating training on unlabeled data.The study uses dijet events with 45 GeV < pT < 55 GeV and |η| < 2.1.Source: §3 · p. 6
- The weakly supervised classifier matches the fully supervised network on simulated data and avoids the standard procedure’s 10% bias under distorted pseudo-data.Figure 3 compares same-population simulated training and a pseudo-data test setting.Source: Figure 3 · p. 6, §3 · p. 7
- Combining the three observables in a neural network consistently outperforms the individual observables across high- and low-gluon-efficiency regimes.The reported comparison uses constituent count, jet width, and leading-subjet pT fraction.Source: §3 · pp. 6–7
- Figure 4 compares five individual features with their combinations using fully supervised and weakly supervised classifiers.The conclusion describes this as an extension from three illustrative features to five.Source: Figure 4 · p. 7
4 Conclusions
The paper presents neural-network classification using known class proportions when individual labels are unavailable, and demonstrates it for quark/gluon tagging. The authors describe it as broadly applicable when detailed simulations are unreliable or unavailable, while noting that the examples use few features.
4 Conclusions
- The paper introduces neural-network classification for settings where class proportions are known but individual labels are not readily available.It demonstrates the approach on quark-versus-gluon jet tagging.Source: §4 · p. 7
- The approach is presented as broadly applicable when detailed simulations are unreliable or unavailable.The conclusion frames quark/gluon and related contexts as cases where it can use unlabeled data rather than labeled, unreliable simulation.Source: §4 · pp. 7–8
- The examples use few input features, and studying extensions to tens or hundreds of features is left for future work.The conclusion says there is no algorithmic limitation on feature count, while identifying larger-feature studies as future work.Source: §4 · p. 8