The NFLikelihood: an unsupervised DNNLikelihood from Normalizing Flows

TL;DR

It is shown, through realistic examples, how Autoregressive Flows, based on affine and rational quadratic spline bijectors, are able to learn complicated high-dimensional Likelihoods arising in High Energy Physics (HEP) analyses.

Abstract

We propose the NFLikelihood, an unsupervised version, based on Normalizing Flows, of the DNNLikelihood proposed in Ref.[1]. We show, through realistic examples, how Autoregressive Flows, based on affine and rational quadratic spline bijectors, are able to learn complicated high-dimensional Likelihoods arising in High Energy Physics (HEP) analyses. We focus on a toy LHC analysis example already considered in the literature and on two Effective Field Theory fits of flavor and electroweak observables, whose samples have been obtained throught the HEPFit code. We discuss advantages and disadvantages of the unsupervised approach with respect to the supervised one and discuss possible interplays of the two.

Figures (5)

• Figure 1: Corner plot of the 1D and 2D marginal posterior distributions of a representative selection of the Toy Likelihood parameters.The true distribution is depicted in red, while the predicted distribution is shown in blue. The solid, dashed and dashed-dotted line over the 1D marginals denote the $68.27\%, 95.45\%$, and $99.73\%$ HPDIs, respectively. The rings on the 2D marginals describe the corresponding probability levels.
• Figure 2: Corner plot of the 1D and 2D marginal posterior distributions of the POIs plus four representative nuisance parameters of the EW Likelihood. The true distribution is depicted in red, while the predicted distribution is shown in blue. The solid, dashed and dashed-dotted line over the 1D marginals denote the $68.27\%, 95.45\%$, and $99.73\%$ HPDIs, respectively. The rings on the 2D marginals describe the corresponding probability levels.
• Figure 3: Corner plot of the 1D and 2D marginal posterior distributions of the Wilson coefficients of the Flavor Likelihood. The true distribution is depicted in red, while the predicted distribution is shown in blue. The solid, dashed and dashed-dotted line over the 1D marginals denote the $68.27\%, 95.45\%$, and $99.73\%$ HPDIs, respectively. The rings on the 2D marginals describe the corresponding probability levels.
• Figure 4: 1D marginal posterior distributions of all the parameters of the Flavor Likelihood. The true distribution is depicted in red, while the predicted distribution is shown in blue. The solid, dashed and dashed-dotted lines over the marginals denote the $68.27\%, 95.45\%$, and $99.73\%$ HPDIs, respectively.
• Figure 5: Correlation matrix of the ElectroWeak fit data.