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.

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

References in corpus (8)

• The global electroweak fit at NNLO and prospects for the LHC and ILC
• Self-Normalizing Neural Networks
• Measurements of properties of the Higgs boson decaying into the four-lepton final state in pp collisions at sqrt(s) = 13 TeV
• 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
• The DNNLikelihood: enhancing likelihood distribution with Deep Learning
• Query Efficient Posterior Estimation in Scientific Experiments via Bayesian Active Learning

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• Reinterpretation of LHC Results for New Physics: Status and Recommendations after Run 2
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• 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