Deep Learning Architectures A Mathematical Approach
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 o
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Ovidiu Calin
Deep Learning Architectures A Mathematical Approach
Springer Series in the Data Sciences Series Editors David Banks, Duke University, Durham, NC, USA Jianqing Fan, Department of Financial Engineering, Princeton University, Princeton, NJ, USA Michael Jordan, University of California, Berkeley, CA, USA Ravi Kannan, Microsoft Research Labs, Bangalore, India Yurii Nesterov, CORE, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium Christopher Ré, Department of Computer Science, Stanford University, Stanford, USA Ryan J. Tibshirani, Department of Statistics, Carnegie Melon University, Pittsburgh, PA, USA Larry Wasserman, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, USA
Springer Series in the Data Sciences focuses primarily on monographs and graduate level textbooks. The target audience includes students and researchers working in and across the fields of mathematics, theoretical computer science, and statistics. Data Analysis and Interpretation is a broad field encompassing some of the fastest-growing subjects in interdisciplinary statistics, mathematics and computer science. It encompasses a process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision making. Data analysis has multiple facets and approaches, including diverse techniques under a variety of names, in different business, science, and social science domains. Springer Series in the Data Sciences addresses the needs of a broad spectrum of scientists and students who are utilizing quantitative methods in their daily research. The series is broad but structured, including topics within all core areas of the data sciences. The breadth of the series reflects the variation of scholarly projects currently underway in the field of machine learning.
More information about this series at http://www.springer.com/series/13852
Ovidiu Calin
Deep Learning Architectures A Mathematical Approach
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Ovidiu Calin Department of Mathematics & Statistics Eastern Michigan University Ypsilanti, MI, USA
ISSN 2365-5674 ISSN 2365-5682 (electronic) Springer Series in the Data Sciences ISBN 978-3-030-36720-6 ISBN 978-3-030-36721-3 (eBook) https://doi.org/10.1007/978-3-030-36721-3 Mathematics Subject Classification (2010): 68T05, 68T10, 68T15, 68T30, 68T45, 68T99 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names a
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