Generalized normalizing flows via Markov chains / Paul Lyonel Hagemann, Johannes Hertrich, Gabriele Steidl.

Format:

Book

Author/Creator:

Hagemann, Paul Lyonel, author.

Hertrich, Johannes, author.

Steidl, Gabriele, author.

Series:

Cambridge elements

Cambridge elements. Elements in non-local data interactions : foundations and applications

Language:

English

Subjects (All):

Markov processes.

Physical Description:

1 online resource (57 pages) : illustrations (black and white, and colour), digital, file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2023.

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.

Notes:

Previously issued in print: 2022.

Includes bibliographical references.

Description based on online resource; title from PDF title page (viewed on February 3, 2023).

Other Format:

Print version :

ISBN:

9781009331012

Access Restriction:

Restricted for use by site license.