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 of interest 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.

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

“…The models are made by learning numbers based on experimental measurements (e.g. likelihoods, posteriors, confidence levels for exclusion) from training data given the parameters of the physical model and experimental nuisance parameters [31]. Such training data can come from experiments or the recasting tools discussed below.…”

“…Such an approach has been proposed in Ref. [31], using a parameterisation that can encode complicated likelihoods with minimal loss of accuracy, in a lightweight, standard, and framework-independent format (e.g. ONNX) suitable for a wide range of reinterpretation applications.…”

“…For scikit-learn, for example, one may serialise the entire model object with the pickle package in Python. Another option, in particular for neural networks, would be to store the model in an ONNX file [31]. The publication of trained ML models for HEP phenomenology is discussed in detail in the contribution by S. Caron et al in Ref.…”

Matrix element regression with deep neural networks — Breaking the CPU barrier

“…[21] and regress on the event information I = − log 10 (weight) instead. Similar approaches have been studied in detail in the literature [36].…”

A guide for deploying Deep Learning in LHC searches: How to achieve optimality and account for uncertainty

“…[45, 67-69, 72, 73, 111-113] for decorrelation techniques, Ref. [24,[28][29][30][31]33,[41][42][43]66,100,[114][115][116][117][118][119] for inference, Ref. [3,4,40,60,109, for tagging, and various other applications in Ref.…”