Learning Likelihood Ratios with Neural Network Classifiers

Abstract

The likelihood ratio is a crucial quantity for statistical inference in science that enables hypothesis testing, construction of confidence intervals, reweighting of distributions, and more. Many modern scientific applications, however, make use of data- or simulation-driven models for which computing the likelihood ratio can be very difficult or even impossible. By applying the so-called ``likelihood ratio trick,'' approximations of the likelihood ratio may be computed using clever parametrizations of neural network-based classifiers. A number of different neural network setups can be defined to satisfy this procedure, each with varying performance in approximating the likelihood ratio when using finite training data. We present a series of empirical studies detailing the performance of several common loss functionals and parametrizations of the classifier output in approximating the likelihood ratio of two univariate and multivariate Gaussian distributions as well as simulated high-energy particle physics datasets.

References in corpus (22)

• PYTHIA 6.4 Physics and Manual
• PYTHIA 6.2 Physics and Manual
• An Introduction to PYTHIA 8.2
• A Brief Introduction to PYTHIA 8.1
• DELPHES 3, A modular framework for fast simulation of a generic collider experiment
• Herwig++ Physics and Manual
• Normalizing Flows: An Introduction and Review of Current Methods
• Herwig 7.0 / Herwig++ 3.0 Release Note
• Anomaly Detection with Density Estimation
• Learning New Physics from a Machine
• OmniFold: A Method to Simultaneously Unfold All Observables
• Constraining Effective Field Theories with Machine Learning
• Simulation Assisted Likelihood-free Anomaly Detection
• A Guide to Constraining Effective Field Theories with Machine Learning
• JUNIPR: a Framework for Unsupervised Machine Learning in Particle Physics
• Neural Networks for Full Phase-space Reweighting and Parameter Tuning
• Reweighting with Boosted Decision Trees
• A guide for deploying Deep Learning in LHC searches: How to achieve optimality and account for uncertainty
• DCTRGAN: Improving the Precision of Generative Models with Reweighting
• E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once
• Parameter Estimation using Neural Networks in the Presence of Detector Effects
• Evidence Networks: simple losses for fast, amortized, neural Bayesian model comparison

Cited by in corpus (10)

• Measurements of $WH$ and $ZH$ production with Higgs boson decays into bottom quarks and direct constraints on the charm Yukawa coupling in $13\mathrm{TeV}$ $pp$ collisions with the ATLAS detector
• Measurement of off-shell Higgs boson production in the $H^{\ast }\to ZZ\to 4\ell$ decay channel using a neural simulation-based inference technique in 13 TeV $pp$ collisions with the ATLAS detector
• Evidence Networks: simple losses for fast, amortized, neural Bayesian model comparison
• Neural Likelihood Surfaces for Spatial Processes with Computationally Intensive or Intractable Likelihoods
• Constraining the Higgs Potential with Neural Simulation-based Inference for Di-Higgs Production
• Interpretable deep learning models for the inference and classification of LHC data
• A Practical Guide to Unbinned Unfolding
• BitHEP -- The Limits of Low-Precision ML in HEP
• Extrapolating Jet Radiation with Autoregressive Transformers
• Finding excesses in model parameter space