[Paper Review] Learning the EFT likelihood with tree boosting

S. Chatterjee, Stefan Rohshap+2 more|arXiv (Cornell University)|May 25, 2022

Nuclear reactor physics and engineering4 citations

TL;DR

This paper introduces a tree-boosting algorithm, Boosted Information Trees (BIT), to learn the likelihood ratio in effective field theory (EFT) analyses for multi-parameter measurements at the LHC. By training on simulated event data with per-event information, BIT approximates the differential cross section ratio order-by-order in Wilson coefficients, achieving near-optimal statistical power comparable to the likelihood ratio test, with significant improvements over baseline $p_{\textrm{T,Z}}$-based methods in exclusion reach.

ABSTRACT

We develop a tree boosting algorithm for collider measurements of multiple Wilson coefficients in effective field theories describing phenomena beyond the standard model of particle physics. The design of the discriminant exploits per-event information of the simulated data sets that encodes the predictions for different values of the Wilson coefficients. This ``Boosted Information Tree'' algorithm provides nearly optimal discrimination power order-by-order in the expansion in the Wilson coefficients and approaches the optimal likelihood ratio test statistic. As a proof-of-principle, we apply the algorithm to the $ extrm{pp} ightarrow extrm{Zh}$ process for different types of modeling.

Motivation & Objective

• To develop a statistically optimal, scalable method for measuring multiple Wilson coefficients in SM-EFT using collider data.
• To overcome the challenge of high-dimensional feature spaces and complex parameter spaces in global EFT fits.
• To enable efficient, order-by-order estimation of the differential cross section ratio using tree-based regression.
• To demonstrate improved exclusion sensitivity compared to conventional $p_{\textrm{T,Z}}$-based strategies in realistic simulation settings.
• To establish a framework that leverages per-event simulation data to train models that approximate the true detector-level likelihood.

Proposed method

• The method uses tree boosting to regress on the differential cross section ratio $\hat{R}(\boldsymbol{x}|\boldsymbol{\theta}, \boldsymbol{\theta}_0)$ as a function of event features $\boldsymbol{x}$, using a mean-squared error (MSE) loss functional.
• It expands the cross section ratio in a Taylor series around $\boldsymbol{\theta}_0$, with each order estimated by a separate boosted tree regressor.
• The weak learner is a CART decision tree, trained on simulated events weighted by the SM-EFT dependence to encode the coefficient functions.
• The boosting algorithm sequentially improves the estimate of $\hat{R}(\boldsymbol{x}|\boldsymbol{\theta}, \boldsymbol{\theta}_0)$ by minimizing the MSE loss over the training data.
• The final test statistic $\hat{q}(\mathcal{D}) = -\log \hat{R}(\boldsymbol{x}|\boldsymbol{\theta}, \boldsymbol{\theta}_0)$ is used for hypothesis testing and exclusion limits.
• A binned version of the estimator is introduced to maintain optimality even when higher-order EFT terms are uncertain, by decoupling training from the coefficients of interest.

Experimental results

Research questions

• RQ1 Can tree boosting be used to learn the likelihood ratio in multi-parameter EFT measurements with near-optimal statistical power?
• RQ2 How well does the Boosted Information Tree (BIT) method approximate the true likelihood ratio under realistic LHC simulation conditions?
• RQ3 Does BIT outperform conventional $p_{\textrm{T,Z}}$-based analysis strategies in terms of exclusion reach for Wilson coefficients?
• RQ4 To what extent does the method remain optimal when higher-order terms in the Wilson coefficient expansion are neglected or uncertain?
• RQ5 Can the BIT framework be applied to realistic event generators including backgrounds and detector effects?

Key findings

• The BIT method achieves nearly optimal discrimination power in hypothesis testing, approaching the performance of the true likelihood ratio test statistic under the Neyman-Pearson lemma.
• In a toy model of the $\mathrm{pp} \to \mathrm{Z}h$ process, the BIT-based test statistic shows optimal power and accurate exclusion contours, validating its theoretical optimality.
• In a realistic MadGraph5_aMC@NLO simulation including backgrounds, BIT significantly improves exclusion reach compared to a $p_{\textrm{T,Z}}$-based strategy with a neural network classifier.
• The binned version of the BIT estimator maintains optimal performance even when higher-order EFT terms are uncertain, by decoupling training from the coefficients of interest.
• The method provides a simple, analytic test statistic with direct interpretability, enabling both binned and unbinned hypothesis testing.
• The algorithm scales efficiently with the number of Wilson coefficients, requiring only as many regressors as the order of the EFT expansion.