An Introduction to Artificial Intelligence Based on Reproducing Kernel Hilbert Spaces (Compact Textbooks in Mathematics) - Softcover

Pereverzyev, Sergei

Softcover

ISBN 10: 3030983153 ISBN 13: 9783030983154

Publisher: Birkhäuser, 2022

Synopsis

This textbook provides an in-depth exploration of statistical learning with reproducing kernels, an active area of research that can shed light on trends associated with deep neural networks. The author demonstrates how the concept of reproducing kernel Hilbert Spaces (RKHS), accompanied with tools from regularization theory, can be effectively used in the design and justification of kernel learning algorithms, which can address problems in several areas of artificial intelligence. Also provided is a detailed description of two biomedical applications of the considered algorithms, demonstrating how close the theory is to being practically implemented.

Among the book’s several unique features is its analysis of a large class of algorithms of the Learning Theory that essentially comprise every linear regularization scheme, including Tikhonov regularization as a specific case. It also provides a methodology for analyzing not only different supervised learning problems, such as regression or ranking, but also different learning scenarios, such as unsupervised domain adaptation or reinforcement learning. By analyzing these topics using the same theoretical framework, rather than approaching them separately, their presentation is streamlined and made more approachable.

An Introduction to Artificial Intelligence Based on Reproducing Kernel Hilbert Spaces is an ideal resource for graduate and postgraduate courses in computational mathematics and data science.

About this title

About the Author

Sergei V. Pereverzyev is Professor and Senior Fellow of the Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences. He is the second recipient of the International Prize for Achievement in Information-Based Complexity (2000), and the inventor of a patented innovation in diabetes technology (2019). He is also the author of two monographs, over one hundred scholarly articles and serves as a member of editorial boards of such international journals as Applied and Computational Harmonic Analysis, Journal of Complexity, Computational Methods in Applied Mathematics, International Journal on Geomathematics, Journal of Diabetes & Metabolism, Frontiers in Applied Mathematics and Statistics, International Journal of Wavelets, Multiresolution and Information Processing. He was principal investigator and person in charge of several research projects granted by research programs FP7 and Horizon-2020, the Austrian Science Fund (FWF), the Austrian Research Promotion Agency (FFG) and the German Research Foundation (DFG).

From the Back Cover

This textbook provides an in-depth exploration of statistical learning with reproducing kernels, an active area of research that can shed light on trends associated with deep neural networks. The author demonstrates how the concept of reproducing kernel Hilbert Spaces (RKHS), accompanied with tools from regularization theory, can be effectively used in the design and justification of kernel learning algorithms, which can address problems in several areas of artificial intelligence. Also provided is a detailed description of two biomedical applications of the considered algorithms, demonstrating how close the theory is to being practically implemented.

Among the book’s several unique features is its analysis of a large class of algorithms of the Learning Theory that essentially comprise every linear regularization scheme, including Tikhonov regularization as a specific case. It also provides a methodology for analyzing not only different supervised learningproblems, such as regression or ranking, but also different learning scenarios, such as unsupervised domain adaptation or reinforcement learning. By analyzing these topics using the same theoretical framework, rather than approaching them separately, their presentation is streamlined and made more approachable.

An Introduction to Artificial Intelligence Based on Reproducing Kernel Hilbert Spaces is an ideal resource for graduate and postgraduate courses in computational mathematics and data science.

Edition details

• Publisher: Birkhäuser
• Publication date: 2022
• Language: English
• ISBN 10: 3030983153
• ISBN 13: 9783030983154
• Binding: Paperback
• Edition number: 1
• Number of pages: 166