Variational And Information Flows In Machine Learning And Optimal Transport
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Variational And Information Flows In Machine Learning And Optimal Transport
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Author : Wuchen Li
language : en
Publisher: Springer Nature
Release Date : 2025-07-18
Variational And Information Flows In Machine Learning And Optimal Transport written by Wuchen Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-18 with Mathematics categories.
This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on “Computational Variational Flows in Machine Learning and Optimal Transport”. Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models.
Variational And Information Flows In Machine Learning And Optimal Transport
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Author : Wuchen Li
language : en
Publisher: Birkhäuser
Release Date : 2025-07-12
Variational And Information Flows In Machine Learning And Optimal Transport written by Wuchen Li and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-12 with Mathematics categories.
This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on “Computational Variational Flows in Machine Learning and Optimal Transport”. Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models.
Information Bottleneck
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Author : Bernhard C. Geiger
language : en
Publisher: MDPI
Release Date : 2021-06-15
Information Bottleneck written by Bernhard C. Geiger and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-15 with Technology & Engineering categories.
The celebrated information bottleneck (IB) principle of Tishby et al. has recently enjoyed renewed attention due to its application in the area of deep learning. This collection investigates the IB principle in this new context. The individual chapters in this collection: • provide novel insights into the functional properties of the IB; • discuss the IB principle (and its derivates) as an objective for training multi-layer machine learning structures such as neural networks and decision trees; and • offer a new perspective on neural network learning via the lens of the IB framework. Our collection thus contributes to a better understanding of the IB principle specifically for deep learning and, more generally, of information–theoretic cost functions in machine learning. This paves the way toward explainable artificial intelligence.
Statistical Optimal Transport
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Author : Sinho Chewi
language : en
Publisher: Springer Nature
Release Date : 2025-05-12
Statistical Optimal Transport written by Sinho Chewi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-12 with Mathematics categories.
This monograph aims to offer a concise introduction to optimal transport, quickly transitioning to its applications in statistics and machine learning. It is primarily tailored for students and researchers in these fields, yet it remains accessible to a broader audience of applied mathematicians and computer scientists. Each chapter is complemented with exercises for the reader to test their understanding. As such, this monograph is suitable for a graduate course on the topic of statistical optimal transport.
Machine Learning And Knowledge Discovery In Databases Research Track
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Author : Albert Bifet
language : en
Publisher: Springer Nature
Release Date : 2024-08-29
Machine Learning And Knowledge Discovery In Databases Research Track written by Albert Bifet and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-29 with Computers categories.
This multi-volume set, LNAI 14941 to LNAI 14950, constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2024, held in Vilnius, Lithuania, in September 2024. The papers presented in these proceedings are from the following three conference tracks: - Research Track: The 202 full papers presented here, from this track, were carefully reviewed and selected from 826 submissions. These papers are present in the following volumes: Part I, II, III, IV, V, VI, VII, VIII. Demo Track: The 14 papers presented here, from this track, were selected from 30 submissions. These papers are present in the following volume: Part VIII. Applied Data Science Track: The 56 full papers presented here, from this track, were carefully reviewed and selected from 224 submissions. These papers are present in the following volumes: Part IX and Part X.
Learning And Intelligent Optimization
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Author : Paola Festa
language : en
Publisher: Springer Nature
Release Date : 2025-01-02
Learning And Intelligent Optimization written by Paola Festa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-02 with Mathematics categories.
This book constitutes the refereed proceedings of the 18th International Conference on Learning and Intelligent Optimization, LION 18, held in Ischia Island, Italy, in June 2024. The 31 full papers and 4 short papers presented in these proceedings were carefully reviewed and selected from 58 submissions. These papers focus on the current research, challenges and applications in the fields of Artificial Intelligent, Machine Learning and Operations Research.
Scale Space And Variational Methods In Computer Vision
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Author : Luca Calatroni
language : en
Publisher: Springer Nature
Release Date : 2023-05-09
Scale Space And Variational Methods In Computer Vision written by Luca Calatroni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-09 with Computers categories.
This book constitutes the proceedings of the 9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023, which took place in Santa Margherita di Pula, Italy, in May 2023. The 57 papers presented in this volume were carefully reviewed and selected from 72 submissions. They were organized in topical sections as follows: Inverse Problems in Imaging; Machine and Deep Learning in Imaging; Optimization for Imaging: Theory and Methods; Scale Space, PDEs, Flow, Motion and Registration.
Generalized Normalizing Flows Via Markov Chains
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Author : Paul Lyonel Hagemann
language : en
Publisher: Cambridge University Press
Release Date : 2023-02-02
Generalized Normalizing Flows Via Markov Chains written by Paul Lyonel Hagemann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-02 with Computers categories.
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.
Scale Space And Variational Methods In Computer Vision
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Author : François Lauze
language : en
Publisher: Springer
Release Date : 2017-05-16
Scale Space And Variational Methods In Computer Vision written by François Lauze and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-16 with Computers categories.
This book constitutes the refereed proceedings of the 6th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2017, held in Kolding, Denmark, in June 2017. The 55 revised full papers presented were carefully reviewed and selected from 77 submissions. The papers are organized in the following topical sections: Scale Space and PDE Methods; Restoration and Reconstruction; Tomographic Reconstruction; Segmentation; Convex and Non-Convex Modeling and Optimization in Imaging; Optical Flow, Motion Estimation and Registration; 3D Vision.
Optimal Transport On Quantum Structures
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Author : Jan Maas
language : en
Publisher: Springer Nature
Release Date : 2024-09-19
Optimal Transport On Quantum Structures written by Jan Maas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-19 with Mathematics categories.
The flourishing theory of classical optimal transport concerns mass transportation at minimal cost. This book introduces the reader to optimal transport on quantum structures, i.e., optimal transportation between quantum states and related non-commutative concepts of mass transportation. It contains lecture notes on classical optimal transport and Wasserstein gradient flows dynamics and quantum optimal transport quantum couplings and many-body problems quantum channels and qubits These notes are based on lectures given by the authors at the "Optimal Transport on Quantum Structures" School held at the Erdös Center in Budapest in the fall of 2022. The lecture notes are complemented by two survey chapters presenting the state of the art in different research areas of non-commutative optimal transport.