Approximating Likelihood Ratios with Calibrated Discriminative Classifiers

Abstract

In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes that tie parameters $\theta$ of an underlying theory and measurement apparatus to high-dimensional observations $\mathbf{x}\in {\mathbb{R}}^p$. However, simulator often do not provide a way to evaluate the likelihood function for a given observation $\mathbf{x}$, which motivates a new class of likelihood-free inference algorithms. In this paper, we show that likelihood ratios are invariant under a specific class of dimensionality reduction maps ${\mathbb{R}}^p\mapsto \mathbb{R}$. As a direct consequence, we show that discriminative classifiers can be used to approximate the generalized likelihood ratio statistic when only a generative model for the data is available. This leads to a new machine learning-based approach to likelihood-free inference that is complementary to Approximate Bayesian Computation, and which does not require a prior on the model parameters. Experimental results on artificial problems with known exact likelihoods illustrate the potential of the proposed method.

35 pages, 5 figures

References in corpus (6)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
• Interpolation between multi-dimensional histograms using a new non-linear moment morphing method
• Top Quark Mass Measurement in the Lepton + Jets Channel Using a Matrix Element Method and in situ Jet Energy Calibration
• Matrix Element Method in HEP: Transfer Functions, Efficiencies, and Likelihood Normalization

Cited by in corpus (81)

• Machine learning and the physical sciences
• The frontier of simulation-based inference
• Deep Learning and its Application to LHC Physics
• Classification without labels: Learning from mixed samples in high energy physics
• Jet Substructure Classification in High-Energy Physics with Deep Neural Networks
• Learning New Physics from a Machine
• Learning in Implicit Generative Models
• OmniFold: A Method to Simultaneously Unfold All Observables
• Mining gold from implicit models to improve likelihood-free inference
• Constraining anomalous Higgs boson couplings to the heavy flavor fermions using matrix element techniques
• Simulation Assisted Likelihood-free Anomaly Detection
• A Guide to Constraining Effective Field Theories with Machine Learning
• Guiding New Physics Searches with Unsupervised Learning
• Decorrelated Jet Substructure Tagging using Adversarial Neural Networks
• Measurements of $WH$ and $ZH$ production in the $H\to b\bar{b}$ decay channel in $pp$ collisions at 13 TeV with the ATLAS detector
• Machine Learning and LHC Event Generation
• Learning to Classify from Impure Samples with High-Dimensional Data
• Hierarchical Implicit Models and Likelihood-Free Variational Inference
• On the Topic of Jets: Disentangling Quarks and Gluons at Colliders
• Neural Networks for Full Phase-space Reweighting and Parameter Tuning
• Simulation-Assisted Decorrelation for Resonant Anomaly Detection
• Mining for Dark Matter Substructure: Inferring subhalo population properties from strong lenses with machine learning
• DisCo Fever: Robust Networks Through Distance Correlation
• Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows
• A Neural Resampler for Monte Carlo Reweighting with Preserved Uncertainties
• Better Higgs Measurements Through Information Geometry
• ABCDisCo: Automating the ABCD Method with Machine Learning
• A guide for deploying Deep Learning in LHC searches: How to achieve optimality and account for uncertainty
• Uncertainty Aware Learning for High Energy Physics
• Fast and Credible Likelihood-Free Cosmology with Truncated Marginal Neural Ratio Estimation
• INFERNO: Inference-Aware Neural Optimisation
• Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling
• Presenting Unbinned Differential Cross Section Results
• A neural simulation-based inference approach for characterizing the Galactic Center $\gamma$-ray excess
• E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once
• LtU-ILI: An All-in-One Framework for Implicit Inference in Astrophysics and Cosmology
• Flows for simultaneous manifold learning and density estimation
• Towards constraining warm dark matter with stellar streams through neural simulation-based inference
• Likelihood-free MCMC with Amortized Approximate Ratio Estimators
• Lightning-Fast Gravitational Wave Parameter Inference through Neural Amortization
• Effective LHC measurements with matrix elements and machine learning
• Neural Approximate Sufficient Statistics for Implicit Models
• Benchmarking Simulation-Based Inference
• Tree boosting for learning EFT parameters
• Adversarial Variational Optimization of Non-Differentiable Simulators
• Likelihood-free inference with an improved cross-entropy estimator
• Dynamic Likelihood-free Inference via Ratio Estimation (DIRE)
• Matrix Element Regression with Deep Neural Networks -- breaking the CPU barrier
• Parameter Estimation using Neural Networks in the Presence of Detector Effects
• Neural Simulation-Based Inference of the Neutron Star Equation of State directly from Telescope Spectra
• Debiasing Standard Siren Inference of the Hubble Constant with Marginal Neural Ratio Estimation
• Subhalo effective density slope measurements from HST strong lensing data with neural likelihood-ratio estimation
• Neural Likelihood Surfaces for Spatial Processes with Computationally Intensive or Intractable Likelihoods
• Search for Flavor Changing Neutral Currents in $t\to Hc,H\to \tau \tau$ Decay at the LHC
• Parameter Inference from Event Ensembles and the Top-Quark Mass
• Fast likelihood-free inference in the LSS Stage IV era
• Uncertainties associated with GAN-generated datasets in high energy physics
• Diagnosing model misspecification and performing generalized Bayes' updates via probabilistic classifiers
• Computationally Inferred Genealogical Networks Uncover Long-Term Trends in Assortative Mating
• Dealing with Nuisance Parameters using Machine Learning in High Energy Physics: a Review
• Improvements to Inference Compilation for Probabilistic Programming in Large-Scale Scientific Simulators
• Neural Conditional Reweighting
• Strategic Plan for a Scientific Software Innovation Institute (S2I2) for High Energy Physics
• Refinable modeling for unbinned SMEFT analyses
• Confidence Sets and Hypothesis Testing in a Likelihood-Free Inference Setting
• Generalized Energy Based Models
• Bayesian technique to combine independently-trained Machine-Learning models applied to direct dark matter detection
• LHC EFT WG Note: SMEFT predictions, event reweighting, and simulation
• Learning to discover: expressive Gaussian mixture models for multi-dimensional simulation and parameter inference in the physical sciences
• Efficient Probabilistic Inference in the Quest for Physics Beyond the Standard Model
• BitHEP -- The Limits of Low-Precision ML in HEP
• Arbitrary Marginal Neural Ratio Estimation for Simulation-based Inference
• Simulation-efficient marginal posterior estimation with swyft: stop wasting your precious time
• Development of systematic uncertainty-aware neural network trainings for binned-likelihood analyses at the LHC
• Probabilistic elicitation of expert knowledge through assessment of computer simulations
• Easy High-Dimensional Likelihood-Free Inference
• Optimal event selection and categorization in high energy physics, Part 1: Signal discovery
• Using holistic event information in the trigger
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories
• Electoral David vs Goliath: How does the Spatial Concentration of Electors affect District-based Elections?
• Generalised Bayes Updates with $f$-divergences through Probabilistic Classifiers