The DNNLikelihood: enhancing likelihood distribution with Deep Learning

Abstract

We introduce the DNNLikelihood, a novel framework to easily encode, through Deep Neural Networks (DNN), the full experimental information contained in complicated likelihood functions (LFs). We show how to efficiently parametrise the LF, treated as a multivariate function of parameters and nuisance parameters with high dimensionality, as an interpolating function in the form of a DNN predictor. We do not use any Gaussian approximation or dimensionality reduction, such as marginalisation or profiling over nuisance parameters, so that the full experimental information is retained. The procedure applies to both binned and unbinned LFs, and allows for an efficient distribution to multiple software platforms, e.g. through the framework-independent ONNX model format. The distributed DNNLikelihood can be used for different use cases, such as re-sampling through Markov Chain Monte Carlo techniques, possibly with custom priors, combination with other LFs, when the correlations among parameters are known, and re-interpretation within different statistical approaches, i.e. Bayesian vs frequentist. We discuss the accuracy of our proposal and its relations with other approximation techniques and likelihood distribution frameworks. As an example, we apply our procedure to a pseudo-experiment corresponding to a realistic LHC search for new physics already considered in the literature.

arXiv comment44 pages, 17 figures, 8 tables; v2: 46 pages, appendix on coverage changed, figures and bibliography improved, references added

References in corpus (29)

• emcee: The MCMC Hammer
• Asymptotic formulae for likelihood-based tests of new physics
• Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)
• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• Learning to Reweight Examples for Robust Deep Learning
• The global electroweak fit at NNLO and prospects for the LHC and ILC
• Don't Decay the Learning Rate, Increase the Batch Size
• Model-independent constraints on Delta F=2 operators and the scale of New Physics
• Self-Normalizing Neural Networks
• A New Approach to a Global Fit of the CKM Matrix
• Updated Global SMEFT Fit to Higgs, Diboson and Electroweak Data
• The 2004 UTfit Collaboration Report on the Status of the Unitarity Triangle in the Standard Model
• Measurements of properties of the Higgs boson decaying into the four-lepton final state in pp collisions at sqrt(s) = 13 TeV
• 2000 CKM-Triangle Analysis A Critical Review with Updated Experimental Inputs and Theoretical Parameters
• O new physics, where art thou? A global search in the top sector
• Adaptive Gradient Methods with Dynamic Bound of Learning Rate
• Compilation of low-energy constraints on 4-fermion operators in the SMEFT
• Electroweak Precision Observables, New Physics and the Nature of a 126 GeV Higgs Boson
• Early stopping and non-parametric regression: An optimal data-dependent stopping rule
• Electroweak precision observables and Higgs-boson signal strengths in the Standard Model and beyond: present and future
• New Physics in $b\to s{\ell }^{+}{\ell }^{-}$ confronts new data on Lepton Universality
• Challenges of Profile Likelihood Evaluation in Multi-Dimensional SUSY Scans
• The DNNLikelihood: enhancing likelihood distribution with Deep Learning
• Query Efficient Posterior Estimation in Scientific Experiments via Bayesian Active Learning
• Decoupling Theoretical Uncertainties from Measurements of the Higgs Boson
• Statistical Challenges for Searches for New Physics at the LHC
• Properties of the Affine Invariant Ensemble Sampler in high dimensions
• The Simplified Likelihood Framework
• Taming systematic uncertainties at the LHC with the central limit theorem

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• Reinterpretation of LHC Results for New Physics: Status and Recommendations after Run 2
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• A guide for deploying Deep Learning in LHC searches: How to achieve optimality and account for uncertainty
• Publishing statistical models: Getting the most out of particle physics experiments
• Higgs boson tagging with the Lund jet plane
• The DNNLikelihood: enhancing likelihood distribution with Deep Learning
• Unbinned multivariate observables for global SMEFT analyses from machine learning
• Constraining dark matter annihilation with cosmic ray antiprotons using neural networks
• Matrix Element Regression with Deep Neural Networks -- breaking the CPU barrier
• A method for approximating optimal statistical significances with machine-learned likelihoods
• Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests
• Simplified likelihoods using linearized systematic uncertainties
• Riemannian Data preprocessing in Machine Learning to focus on QCD color structure