Studies in Big Data 20 Oliver Kramer Machine Learning for Evolution Strategies Studies in Big Data Volume 20 Series editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland e-mail: [email protected] About this Series The series “Studies in Big Data” (SBD) publishes new developments and advances in the various areas of Big Data- quickly and with a high quality. The intent is to cover the theory, research, development, and applications of Big Data, as embedded in the fields of engineering, computer science, physics, economics and life sciences. The books of the series refer to the analysis and understanding of large, complex, and/or distributed data sets generated from recent digital sources coming from sensors or other physical instruments as well as simulations, crowd sourcing, social networks or other internet transactions, such as emails or video click streams and other. The series contains monographs, lecture notes and edited volumes in Big Data spanning the areas of computational intelligence incl. neural networks, evolutionary computation, soft computing, fuzzy systems, as well as artificial intelligence, data mining, modern statistics and Operations research, as well as self-organizing systems. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution, which enable both wide and rapid dissemination of research output. More information about this series at http://www.springer.com/series/11970 Oliver Kramer Machine Learning for Evolution Strategies 123 Oliver Kramer Informatik Universität Oldenburg Oldenburg Germany ISSN 2197-6503 ISSN 2197-6511 (electronic) Studies in Big Data ISBN 978-3-319-33381-6 ISBN 978-3-319-33383-0 (eBook) DOI 10.1007/978-3-319-33383-0 Library of Congress Control Number: 2016938389 © Springer International Publishing Switzerland 2016 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 are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland Contents 1 Introduction ........................................ 1 1.1 Computational Intelligence . 1 1.2 Optimization . 1 1.3 Machine Learning and Big Data . 3 1.4 Motivation . 5 1.5 Benchmark Problems . 5 1.6 Overview . 6 1.7 Previous Work. 8 1.8 Notations . 8 1.9 Python . 9 References . 10 Part I Evolution Strategies 2 Evolution Strategies ................................... 13 2.1 Introduction. 13 2.2 Evolutionary Algorithms . 14 2.3 History . 15 2.4 Recombination. 16 2.5 Mutation. 16 2.6 Selection. 17 2.7 Rechenberg’s 1/5th Success Rule . 18 2.8 (1+1)-ES. 19 2.9 Conclusions . 20 References . 21 3 Covariance Matrix Estimation ........................... 23 3.1 Introduction. 23 3.2 Covariance Matrix Estimation . 24 3.3 Algorithm . 25 3.4 Related Work . 26 v vi Contents 3.5 Experimental Analysis . 27 3.6 Conclusions . 30 References . 31 Part II Machine Learning 4 Machine Learning .................................... 35 4.1 Introduction. 35 4.2 Prediction and Inference . 36 4.3 Classification. 37 4.4 Model Selection. 38 4.5 Curse of Dimensionality . 39 4.6 Bias-Variance Trade-Off . 40 4.7 Feature Selection and Extraction . 41 4.8 Conclusions . 42 References . 43 5 Scikit-Learn......................................... 45 5.1 Introduction. 45 5.2 Data Management . 46 5.3 Supervised Learning. 47 5.4 Pre-processing Methods . 48 5.5 Model Evaluation. 49 5.6 Model Selection. 50 5.7 Unsupervised Learning . 51 5.8 Conclusions . 52 Reference . 53 Part III Supervised Learning 6 Fitness Meta-Modeling ................................. 57 6.1 Introduction. 57 6.2 Nearest Neighbors . 58 6.3 Algorithm . 59 6.4 Related Work . 60 6.5 Experimental Analysis . 61 6.6 Conclusions . 64 References . 64 7 Constraint Meta-Modeling .............................. 67 7.1 Introduction. 67 7.2 Support Vector Machines . 68 7.3 Algorithm . 71 7.4 Related Work . 72 Contents vii 7.5 Experimental Analysis . 73 7.6 Conclusions . 75 References . 75 Part IV Unsupervised Learning 8 Dimensionality Reduction Optimization..................... 79 8.1 Introduction. 79 8.2 Dimensionality Reduction . 80 8.3 Principal Component Analysis . 80 8.4 Algorithm . 82 8.5 Related Work . 83 8.6 Experimental Analysis . 84 8.7 Conclusions . 86 References . 87 9 Solution Space Visualization............................. 89 9.1 Introduction. 89 9.2 Isometric Mapping . 90 9.3 Algorithm . 92 9.4 Related Work . 93 9.5 Experimental Analysis . 94 9.6 Conclusions . 96 References . 97 10 Clustering-Based Niching ............................... 99 10.1 Introduction. 99 10.2 Clustering . 100 10.3 Algorithm . 101 10.4 Related Work . 102 10.5 Experimental Analysis . 103 10.6 Conclusions . 106 References . 106 Part V Ending 11 Summary and Outlook................................. 111 11.1 Summary . ..