The DNNLikelihood: enhancing likelihood distribution with Deep Learning
  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.
