[Paper Review] Classifying Anomalies THrough Outer Density Estimation (CATHODE)

Anna Hallin, Joshua Isaacson+7 more|arXiv (Cornell University)|Sep 1, 2021

Particle physics theoretical and experimental studies54 references25 citations

TL;DR

CATHODE is a model-agnostic LHC anomaly detection strategy that uses outer density estimation with a conditional density model to generate background-like samples in the signal region, then trains a classifier to distinguish data from the background model, achieving near-optimal anomaly detection performance on LHCO R&D data.

ABSTRACT

We propose a new model-agnostic search strategy for physics beyond the standard model (BSM) at the LHC, based on a novel application of neural density estimation to anomaly detection. Our approach, which we call Classifying Anomalies THrough Outer Density Estimation (CATHODE), assumes the BSM signal is localized in a signal region (defined e.g. using invariant mass). By training a conditional density estimator on a collection of additional features outside the signal region, interpolating it into the signal region, and sampling from it, we produce a collection of events that follow the background model. We can then train a classifier to distinguish the data from the events sampled from the background model, thereby approaching the optimal anomaly detector. Using the LHC Olympics R&D dataset, we demonstrate that CATHODE nearly saturates the best possible performance, and significantly outperforms other approaches that aim to enhance the bump hunt (CWoLa Hunting and ANODE). Finally, we demonstrate that CATHODE is very robust against correlations between the features and maintains nearly-optimal performance even in this more challenging setting.

Motivation & Objective

• Motivate a model-agnostic search strategy for BSM physics at the LHC that complements traditional targeted analyses.
• Develop a method that learns background distributions from outer (sideband) regions and samples into the signal region to enable robust anomaly detection.
• Demonstrate that the method approaches the theoretical optimum for data-vs-background anomaly detection and is robust to correlations between features.
• Compare performance against bump-hunt–based enhancements (CWOLA Hunting) and density-estimation–based approaches (A-node).
• Quantify the benefits of oversampling the background model and assess robustness under feature-msignal correlations.

Proposed method

• Train a conditional density estimator on the outer (sideband) region using Masked Autoregressive Flows (MAF) to model p(x|m not in SR).
• Interpolate the learned outer density into the signal region by sampling from the interpolated background density to produce background-like events in SR.
• Train a classifier to distinguish data in SR from the sampled background events, thereby approximating the likelihood ratio p_data(x|m)/p_bg(x|m).
• Use an ensemble of model states (10 epochs) for density estimation and classifier predictions to stabilize results.
• Oversample the background model by generating a large set of synthetic background events to improve classifier training and anomaly sensitivity.
• Evaluate performance using the Significance Improvement Characteristic (SIC) and compare against CWOLA Hunting, A-node, idealized anomaly detector, and a fully supervised classifier.
• Handle feature preprocessing (logit transform, standardization) and KDE-based sampling of m_JJ to ensure consistent sampling in SR.

Experimental results

Research questions

• RQ1 Can CATHODE approach the optimal likelihood-ratio detector in a data-vs-background anomaly detection setting?
• RQ2 How does CATHODE perform compared to bump-hunt–based enhancements (CWOLA Hunting) and pure density-estimation approaches (A-node) across signal strengths?
• RQ3 Is CATHODE robust to correlations between auxiliary features x and the bump-variable m_JJ (in SR and SB) that challenge other methods?
• RQ4 What is the impact of oversampling the background model on anomaly detection performance, and what is the optimal sampling size?
• RQ5 How does CATHODE perform when the signal-to-background ratio (S/B) varies, especially at low S/B?

Key findings

• CATHODE outperforms CWOLA Hunting and A-node across a wide range of signal efficiencies on the LHCO R&D dataset.
• The method achieves a maximum SIC around 14, surpassing A-node (≈6.5) and CWOLA Hunting (≈11).
• CATHODE’s performance approaches that of an idealized anomaly detector, indicating near-saturation of the theoretical upper bound in this setting.
• The approach remains robust against correlations between x and m_JJ, unlike CWOLA Hunting which degrades substantially under correlation.
• Oversampling the background model (e.g., using about 200k synthetic SR background events) significantly improves SIC, with diminishing returns beyond certain sampling sizes.