Institute for Advanced Study / Princeton University Joint Astrophysics Colloquium

Normalizing Flows (NF) are bijective maps from the data to a Gaussian (normal) distribution or viceversa. In contrast to other generative models they are lossless and provide data likelihood via the Jacobian of the transformation. I will first present a novel Sliced NF (SNF), which is based on Optimal Transport theory, achieving state of the art results in density estimation for small data samples. I will present its applications to Bayesian Inference and to Global Optimization problems, where SNF enables new methods of sampling and optimization that eliminate the need for sequential Monte Carlo Markov Chains (MCMC), and have the potential to be much faster than MCMC. In the second half of the talk I will generalize this approach to data structures with physics symmetries, focusing on Rotational and Translational Equivariance Normalizing Flow (TRENF), which can be used for generative modeling and likelihood analysis of cosmological data. By training the data likelihood on the posterior this approach enables near optimal cosmological likelihood analysis, where information from all the data is optimally combined into a single number (likelihood)as a function of cosmological parameters. This method provides uncertainty quantification via the full posterior of cosmological parameters, which paves the way for a complete and optimal data analysis with Normalizing Flows.

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