mlsanityData to 14 Oct 2026

Learning Likelihood Ratios with Neural Network Classifiers

arXiv 2305.10500 ↗First posted 17 May 2023hep-ph physics.data-an stat.APcited by 11

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 22 of its 60 references that are in the map. First posted on arXiv 17 May 2023.

Builds on

22 of 60 references.

References · 22

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2015Variational Inference with Normalizing Flowscited by 2,170
  4. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  5. 2017Self-Normalizing Neural Networkscited by 598
  6. 2015Approximating Likelihood Ratios with Calibrated Discriminative Classifierscited by 90
  7. 2020Anomaly Detection with Density Estimationcited by 72
  8. 2019MadMiner: Machine learning-based inference for particle physicscited by 32
  9. 2019OmniFold: A Method to Simultaneously Unfold All Observablescited by 31
  10. 2020Simulation Assisted Likelihood-free Anomaly Detectioncited by 27
  11. 2018Constraining Effective Field Theories with Machine Learningcited by 26
  12. 2018A Guide to Constraining Effective Field Theories with Machine Learningcited by 25
10 more
  1. 2020DCTRGAN: Improving the Precision of Generative Models with Reweightingcited by 22
  2. 2019Neural Networks for Full Phase-space Reweighting and Parameter Tuningcited by 20
  3. 2018JUNIPR: a Framework for Unsupervised Machine Learning in Particle Physicscited by 18
  4. 2019Training Neural Networks for Likelihood/Density Ratio Estimationcited by 17
  5. 2021E Pluribus Unum Ex Machina: Learning from Many Collider Events at Oncecited by 15
  6. 2018Likelihood-free inference with an improved cross-entropy estimatorcited by 11
  7. 2016Reweighting with Boosted Decision Treescited by 10
  8. 2022Contrastive Neural Ratio Estimation for Simulation-based Inferencecited by 7
  9. 2020Parameter Estimation using Neural Networks in the Presence of Detector Effectscited by 6
  10. 2023Flow Away your Differences: Conditional Normalizing Flows as an Improvement to Reweightingcited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 3; 2026: 3.

11 papers.

  1. 2023Evidence Networks: simple losses for fast, amortized, neural Bayesian model comparisoncited by 10
  2. 2024Optimal Equivariant Architectures from the Symmetries of Matrix-Element Likelihoodscited by 5
  3. 2024Constraining the Higgs Potential with Neural Simulation-based Inference for Di-Higgs Productioncited by 4
  4. 2025Uncertainty-Aware Likelihood Ratio Estimation for Pixel-Wise Out-of-Distribution Detectioncited by 3
  5. 2024Extrapolating Jet Radiation with Autoregressive Transformerscited by 2
  6. 2024Classification under Nuisance Parameters and Generalized Label Shift in Likelihood-Free Inferencecited by 1
  7. 2025BitHEP -- The Limits of Low-Precision ML in HEPcited by 1
  8. 2026Temper-Then-Tilt: Principled Unlearning for Generative Models through Tempering and Classifier Guidancecited by 1
  9. 2026Conditional Neural Bayes Ratio Estimation for Experimental Design Optimisationcited by 1
  10. 2026An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learningcited by 1
  11. 2025Quasiprobabilistic Density Ratio Estimation with a Reverse Engineered Classification Loss Functioncited by 0