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Series:   Elements in Non-local Data Interactions: Foundations and Applications

Generalized Normalizing Flows via Markov Chains

Published online by Cambridge University Press:  19 January 2023

Paul Lyonel Hagemann ,
Johannes Hertrich  and
Gabriele Steidl
Paul Lyonel Hagemann
Affiliation:
Technische Universität Berlin
Johannes Hertrich
Affiliation:
Technische Universität Berlin
Gabriele Steidl
Affiliation:
Technische Universität Berlin

Summary

Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This Element provides a unified framework to handle these approaches via Markov chains. The authors consider stochastic normalizing flows as a pair of Markov chains fulfilling some properties, and show how many state-of-the-art models for data generation fit into this framework. Indeed numerical simulations show that including stochastic layers improves the expressivity of the network and allows for generating multimodal distributions from unimodal ones. The Markov chains point of view enables the coupling of both deterministic layers as invertible neural networks and stochastic layers as Metropolis-Hasting layers, Langevin layers, variational autoencoders and diffusion normalizing flows in a mathematically sound way. The authors' framework establishes a useful mathematical tool to combine the various approaches.
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Keywords

normalizing flowsvariational autoencodersinvertible neural networksMarkov kernelsMarkov chain Monto Carlo methods
Type
Element
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Series: Elements in Non-local Data Interactions: Foundations and Applications
Online ISBN: 9781009331012
Publisher: Cambridge University Press
Print publication: 02 February 2023

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