This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter.
This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.
Arvustused
This book is useful to students who have already had an introductory course in machine learning and are further interested to deepen their understanding of the machine learning material from the mathematical point of view. (T. C. Mohan, zbMATH 1441.68001, 2020)
Introductory Problems.- Activation Functions.- Cost Functions.- Finding
Minima Algorithms.- Abstract Neurons.- Neural Networks.- Approximation
Theorems.- Learning with One-dimensional Inputs.- Universal
Approximators.- Exact Learning.- Information Representation.- Information
Capacity Assessment.- Output
Manifolds.- Neuromanifolds.- Pooling.- Convolutional Networks.- Recurrent
Neural Networks.- Classification.- Generative Models.- Stochastic
Networks.- Hints and Solutions.
Ovidiu Calin, a graduate from University of Toronto, is a professor at Eastern Michigan University and a former visiting professor at Princeton University and University of Notre Dame. He has delivered numerous lectures at several universities in Japan, Hong Kong, Taiwan, and Kuwait over the last 15 years. His publications include over 60 articles and 8 books in the fields of machine learning, computational finance, stochastic processes, variational calculus and geometric analysis.
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