{"product_id":"generalized-normalizing-flows-via-markov-chains-paperback-9781009331005","title":"Generalized Normalizing Flows via Markov Chains (Paperback \/ softback) 9781009331005","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eGeneralized Normalizing Flows via Markov Chains\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis Element provides a unified framework to handle various approaches to generative models via Markov chains.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003ePaul Lyonel Hagemann (Author), Johannes Hertrich (Author), Gabriele Steidl (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009331005, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 2 February 2023\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e75 pages\u003cbr\u003e22.9 x 15.2 x 0.4 cm, 0.094 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eNormalizing 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. Preliminaries\u003cbr\u003e 3. Normalizing Flows\u003cbr\u003e 4. Stochastic Normalizing Flows\u003cbr\u003e 5. Stochastic Layers\u003cbr\u003e 6. Conditional Generative Modeling\u003cbr\u003e 7. Numerical Results\u003cbr\u003e 8. Conclusions and Open Questions\u003cbr\u003e References.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Stochastics [\u003ca title=\"See our other books on Stochastics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Stochastics%20%5BPBWL%5D%22\"\u003ePBWL\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46265425068312,"sku":"9781009331005","price":17.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781009331005i_6939fc4c-f162-48ee-b169-456719dae19a.jpg?v=1696791946","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/generalized-normalizing-flows-via-markov-chains-paperback-9781009331005","provider":"Freshly Printed Books","version":"1.0","type":"link"}