The NFLikelihood: an unsupervised DNNLikelihood from Normalizing Flows

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.