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Assessing and Improving Prediction and Classification
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Title: Assessing and Improving Prediction and Classification: Theory and Algorithms in C++ Author: Timothy Masters Length: 517 pages Edition: 1st ed. Language: English Publisher: Apress Publication Date: 2017-12-20 ISBN-10: 1484233352 ISBN-13: 9781484233351
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Assessing and
Improving Prediction
and Classification
Theory and Algorithms in C++
TimothyMasters
Assessing and Improving Prediction and Classication: eory and Algorithms
in C++
ISBN-13 (pbk): 978-1-4842-3335-1 ISBN-13 (electronic): 978-1-4842-3336-8
https://doi.org/10.1007/978-1-4842-3336-8
Library of Congress Control Number: 2017962869
Copyright © 2018 by Timothy Masters
is work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the
material is concerned, specically the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microlms 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.
Trademarked names, logos, and images may appear in this book. Rather than use a trademark symbol with
every occurrence of a trademarked name, logo, or image we use the names, logos, and images only in an
editorial fashion and to the benet of the trademark owner, with no intention of infringement of the
trademark.
e use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not
identied as such, is not to be taken as an expression of opinion as to whether or not they are subject to
proprietary rights.
While the advice and information in this book are believed to be true and accurate at the date of publication,
neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or
omissions that may be made. e publisher makes no warranty, express or implied, with respect to the
material contained herein.
Cover image by Freepik (www.freepik.com)
Managing Director: Welmoed Spahr
Editorial Director: Todd Green
Acquisitions Editor: Steve Anglin
Development Editor: Matthew Moodie
Technical Reviewers: Massimo Nardone and Matt Wiley
Coordinating Editor: Mark Powers
Copy Editor: Kim Wimpsett
Distributed to the book trade worldwide by Springer Science+Business Media NewYork, 233 Spring Street,
6th Floor, NewYork, NY 10013. Phone 1-800-SPRINGER, fax (201) 348-4505, e-mail orders-ny@springer-
sbm.com, or visit www.springeronline.com. Apress Media, LLC is a California LLC and the sole member
(owner) is Springer Science + Business Media Finance Inc (SSBM Finance Inc). SSBM Finance Inc is a
Delaware corporation.
For information on translations, please e-mail rights@apress.com, or visit www.apress.com/
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Any source code or other supplementary material referenced by the author in this book is available to
readers on GitHub via the book’s product page, located at www.apress.com/9781484233351. For more
detailed information, please visit www.apress.com/source-code.
Printed on acid-free paper
TimothyMasters
Ithaca, New York, USA
is book is dedicated to Master Hidy Ochiai with the utmost respect,
admiration, and gratitude. His incomparable teaching of Washin-Ryu
karate has raised my condence, my physical ability, and my mental
acuity far beyond anything I could have imagined.
For this I will ever be grateful.
v
About the Author ��������������������������������������������������������������������������������������������������� xiii
About the Technical Reviewers �������������������������������������������������������������������������������xv
Preface ������������������������������������������������������������������������������������������������������������������xvii
Table of Contents
Chapter 1: Assessment ofNumeric Predictions ������������������������������������������������������� 1
Notation......................................................................................................................................... 2
Overview ofPerformance Measures ............................................................................................. 3
Consistency andEvolutionary Stability .................................................................................... 6
Selection Bias andtheNeed forThree Datasets........................................................................... 9
Cross Validation andWalk-Forward Testing ................................................................................ 14
Bias inCross Validation ......................................................................................................... 15
Overlap Considerations.......................................................................................................... 15
Assessing Nonstationarity Using Walk-Forward Testing........................................................ 17
Nested Cross Validation Revisited ......................................................................................... 18
Common Performance Measures ................................................................................................ 20
Mean Squared Error .............................................................................................................. 20
Mean Absolute Error .............................................................................................................. 23
R-Squared ............................................................................................................................. 23
RMS Error .............................................................................................................................. 24
Nonparametric Correlation .................................................................................................... 24
Success Ratios ...................................................................................................................... 26
Alternatives toCommon Performance Measures .................................................................. 27
Stratication forConsistency ...................................................................................................... 27
Condence Intervals ................................................................................................................... 29
The Condence Set ............................................................................................................... 30
Serial Correlation ................................................................................................................... 32
vi
Multiplicative Data ................................................................................................................. 32
Normally Distributed Errors ................................................................................................... 33
Empirical Quantiles asCondence Intervals ............................................................................... 35
Condence Bounds forQuantiles .......................................................................................... 37
Tolerance Intervals ................................................................................................................ 40
Chapter 2: Assessment ofClass Predictions ���������������������������������������������������������� 45
The Confusion Matrix .................................................................................................................. 46
Expected Gain/Loss ............................................................................................................... 46
ROC (Receiver Operating Characteristic) Curves ........................................................................ 48
Hits, False Alarms, andRelated Measures ............................................................................ 48
Computing theROC Curve ..................................................................................................... 50
Area Under theROC Curve ..................................................................................................... 56
Cost andtheROC Curve ........................................................................................................ 59
Optimizing ROC-Based Statistics ................................................................................................ 60
Optimizing theThreshold: Now or Later? .............................................................................. 61
Maximizing Precision ............................................................................................................ 64
Generalized Targets ............................................................................................................... 65
Maximizing Total Gain ............................................................................................................ 66
Maximizing Mean Gain .......................................................................................................... 67
Maximizing theStandardized Mean Gain .............................................................................. 67
Condence inClassication Decisions ....................................................................................... 69
Hypothesis Testing ................................................................................................................. 70
Condence intheCondence ................................................................................................ 75
Bayesian Methods ................................................................................................................. 81
Multiple Classes .................................................................................................................... 85
Hypothesis Testing vs. Bayes’ Method .................................................................................. 86
Final Thoughts onHypothesis Testing ................................................................................... 91
Condence Intervals forFuture Performance ............................................................................. 98
Table of ConTenTs
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