Uros Seljak (UC Berkeley)
Title: Normalizing Flows for cosmology, particle physics, and statistical inference
Abstract:
Normalizing flows (NF) are bijective maps from the data to a Gaussian (normal) distribution. In contrast to other generative models such as GANs they are lossless and provide data likelihood via the Jacobian of the transformation. I will first present a novel Sliced Iterative NF (SINF), which is based on Sliced Optimal Transport. I will show that it achieves state of the art results, and in contrast to other Deep Learning NFs, it is iterative, easy to use and has very few
hyperparameters. I will present two applications: first one is to the HEP blind challenge LHC Olympics 2020, where SINF was the winning entry. Second is to
applications in Bayesian statistical inference, where SINF enables new methods of sampling and evidence calculations that eliminate the need for Markov Chains. In the second half of the talk I will generalize this approach to data structures with symmetries. I will introduce Rotational and Translational Equivariance NF (TRENF), which can be used for generative modeling and data analysis of cosmological data. I will argue that this approach enables optimal cosmological data analysis, where information from all the cumulants is optimally combined into a single number, the data likelihood as a function of cosmological parameters. This also provides uncertainty
quantification via the posterior analysis.