Numerical Machine Learning - Zhiyuan Wang - E-Book

Numerical Machine Learning E-Book

Zhiyuan Wang

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Beschreibung

Numerical Machine Learning is a simple textbook on machine learning that bridges the gap between mathematics theory and practice. The book uses numerical examples with small datasets and simple Python codes to provide a complete walkthrough of the underlying mathematical steps of seven commonly used machine learning algorithms and techniques, including linear regression, regularization, logistic regression, decision trees, gradient boosting, Support Vector Machine, and K-means Clustering.

Through a step-by-step exploration of concrete numerical examples, the students (primarily undergraduate and graduate students studying machine learning) can develop a well-rounded understanding of these algorithms, gain an in-depth knowledge of how the mathematics relates to the implementation and performance of the algorithms, and be better equipped to apply them to practical problems.

Key features

- Provides a concise introduction to numerical concepts in machine learning in simple terms

- Explains the 7 basic mathematical techniques used in machine learning problems, with over 60 illustrations and tables

- Focuses on numerical examples while using small datasets for easy learning

- Includes simple Python codes

- Includes bibliographic references for advanced reading

The text is essential for college and university-level students who are required to understand the fundamentals of machine learning in their courses.

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Seitenzahl: 131

Veröffentlichungsjahr: 2000

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Table of Contents
BENTHAM SCIENCE PUBLISHERS LTD.
End User License Agreement (for non-institutional, personal use)
Usage Rules:
Disclaimer:
Limitation of Liability:
General:
PREFACE
Introduction to Machine Learning
Abstract
1.1. BRIEF HISTORY OF MACHINE LEARNING
1.2. MACHINE LEARNING AS A DE FACTO FEATURE
1.3. SUPERVISED AND UNSUPERVISED
1.4. REGRESSION AND CLASSIFICATION
1.5. UNDERFITTING AND OVERFITTING
1.6. THE IMPORTANCE OF UNDERSTANDING MACHINE LEARNING THROUGH NUMERICAL EXAMPLE
CONCLUSION
REFERENCES
Linear Regression
Abstract
2.1. INTRODUCTION TO LINEAR REGRESSION
2.2. MATHEMATICS OF LINEAR REGRESSION
2.3. NUMERICAL EXAMPLE OF LINEAR REGRESSION
2.3.1. Start the First Iteration of Learning
CONCLUSION
References
Regularization
Abstract
3.1. INTRODUCTION TO L1 AND L2 REGULARIZATION
3.2. MATHEMATICS OF L1 REGULARIZATION FOR LINEAR REGRESSION
3.3. NUMERICAL EXAMPLE OF L1 REGULARIZATION FOR LINEAR REGRESSION
3.3.1. Start the First Iteration of Learning
3.3.2. End the First Iteration of Learning
3.3.3. Start the Second Iteration of Learning
3.3.4. End the Second Iteration of Learning
3.4. SAMPLE CODES AND COMPARISON OF L1 REGULARIZATION FOR LINEAR REGRESSION
3.5. MATHEMATICS OF L2 REGULARIZATION FOR LINEAR REGRESSION
3.6. NUMERICAL EXAMPLE OF L2 REGULARIZATION FOR LINEAR REGRESSION
3.6.1. Start the First Iteration of Learning
3.6.2. End the First Iteration of Learning
3.6.3. Start the Second Iteration of Learning
3.6.4. End the Second Iteration of Learning
3.7. SAMPLE CODES AND COMPARISON OF L2 REGULARIZATION FOR LINEAR REGRESSION
CONCLUSION
References
Logistic Regression
Abstract
4.1. INTRODUCTION TO LOGISTIC REGRESSION
4.2. MATHEMATICS OF LOGISTIC REGRESSION
4.3. NUMERICAL EXAMPLE OF LOGISTIC REGRESSION
4.3.1. Start the First Iteration of Learning
4.3.2. End the First Iteration of Learning
4.3.3. Start the Second Iteration of Learning
4.3.4. End the Second Iteration of Learning
4.4. SAMPLE CODES AND COMPARISON
CONCLUSION
References
Decision Tree
Abstract
5.1.. INTRODUCTION TO DECISION TREE
5.2.. ALGORITHM OF DECISION TREE
5.3.. NUMERICAL EXAMPLE OF DECISION TREE
5.4.. SAMPLE CODES AND COMPARISON
CONCLUSION
References
Gradient Boosting
Abstract
6.1. INTRODUCTION TO GRADIENT BOOSTING
6.2. MATHEMATICS OF GRADIENT BOOSTING FOR REGRESSION
6.3. NUMERICAL EXAMPLE AND CODE COMPARISON OF GRADIENT BOOSTING FOR REGRESSION
6.4. MATHEMATICS OF GRADIENT BOOSTING FOR CLASSI-FICATION
6.5. Numerical Example and Code Comparison of Gradient Boosting for Classification
CONCLUSION
References
Support Vector Machine
Abstract
7.1. INTRODUCTION TO SUPPORT VECTOR MACHINE
7.2. MATHEMATICS OF SUPPORT VECTOR MACHINE: LINEARLY SEPARABLE CASE
7.3. NUMERICAL EXAMPLE AND CODE COMPARISON OF SUPPORT VECTOR MACHINE: LINEARLY SEPARABLE CASE
7.4. MATHEMATICS OF SUPPORT VECTOR MACHINE: LINEARLY NON-SEPARABLE CASE
7.5. NUMERICAL EXAMPLE AND CODE COMPARISON OF SUPPORT VECTOR MACHINE: LINEARLY NON-SEPARABLE CASE USING POLYNOMIAL KERNEL
7.6. NUMERICAL EXAMPLE AND CODE COMPARISON OF SUPPORT VECTOR MACHINE: LINEARLY NON-SEPARABLE CASE USING RADIAL BASIS FUNCTION KERNEL
CONCLUSION
REFERENCES
K-means Clustering
Abstract
8.1. INTRODUCTION TO CLUSTERING AND DISTANCE METRICS
8.1.1. Euclidean Distance
8.1.2. Manhattan Distance
8.1.3. Cosine Similarity
8.1.4. Chebyshev Distance
8.2. ALGORITHM OF K-MEANS CLUSTERING
8.3. NUMERICAL EXAMPLE OF K-MEANS CLUSTERING
8.4. SAMPLE CODES AND COMPARISON
CONCLUSION
REFERENCES
Numerical Machine Learning
Authored by:
Zhiyuan Wang
DigiPen Institute of Technology Singapore Singapore
National University of Singapore Singapore
Sayed Ameenuddin Irfan
DigiPen Institute of Technology Singapore Singapore
National University of Singapore Singapore
Sayed Ameenuddin Irfan
DigiPen Institute of Technology Singapore
Singapore
&
Priyanka Hriday Bhoyar
DigiPen Institute of Technology Singapore Singapore

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PREFACE

In recent years, machine learning has become increasingly popular and pervasive, with applications ranging from self-driving cars and facial recognition to personalized website recommendations and stock market forecasting. The increased availability of data and advancements in computer power have made it possible to apply machine learning algorithms to a vast array of problems with impressive outcomes. Machine learning is currently utilized in a variety of areas, including banking, healthcare, marketing, and manufacturing, and it is anticipated that it will continue to play a significant role in the development of new technologies in the future. Consequently, machine learning has emerged as an essential subject of study for people interested in data science, artificial intelligence, and related fields. As machine learning continues to evolve and expand its reach, researchers and practitioners are constantly developing new techniques and algorithms to address specific challenges or improve upon existing methods. In this ever-changing landscape, it is crucial for those working in the field to stay up-to-date with the latest advancements and trends. This includes not only mastering the fundamental concepts and algorithms, but also understanding how to adapt and apply them in novel ways to solve real-world problems. By embracing the interdisciplinary nature of machine learning, and collaborating with experts from diverse fields, we can accelerate the development of innovative solutions that have the potential to transform industries, enhance the quality of life, and create a more sustainable future for all.

From our experiences of teaching machine learning using various textbooks, we have noticed that there tends to be a strong emphasis on abstract mathematics when discussing the theories of machine learning algorithms. On the other hand, in the application of machine learning, it usually straightaway goes to import offthe- shelf libraries such as scikit-learn, TensorFlow, Keras, and PyTorch. The disconnect between abstract mathematical theories and practical application creates a gap in understanding. This book bridges the gap using numerical examples with small datasets and simple Python codes to provide a complete walkthrough of the underlying mathematical steps of machine learning algorithms. By working through concrete examples step by step, readers/students can develop a well-rounded understanding of these algorithms, gain a more indepth knowledge of how mathematics relates to the implementation and performance of the algorithms, and be better equipped to apply them to practical problems.

Beginning with an introduction to machine learning in Chapter 1, the remaining chapters of the book cover seven commonly used machine learning algorithms and techniques, including both supervised and unsupervised learning, as well as both linear and nonlinear models. The book requires some prerequisite knowledge of basic probability and statistics, linear algebra, calculus, and Python programming. The book is intended for university students studying machine learning and is used as our primary teaching material for the “Introduction to Machine Learning” module at DigiPen Institute of Technology Singapore.

In conclusion, we would like to acknowledge Mr. Tan Chek Ming (Managing Director), Prof. Prasanna Ghali (Provost), Ms. Caroline Tan (Deputy Director), Ms. Angela Tay (Senior Manager), and all at DigiPen Institute of Technology Singapore, for their consistent support and help. We also wish to thank a number of our students (including Nelson Ng, Rhonda McGladdery, Farhan Fadzil, Lim Li Jia, Musa Ahmad Dahlan, Jeremy Yap, and Seah Jue Chen) for their diligence in spotting several typographical errors during their course of studies. Also, it has been a delight working with Bentham's professional editorial and production staff. We particularly thank Noor Ul Ain Khan, Humaira Hashmi, and Obaid Sadiq for their consistent, timely, and kind support throughout the development of this book. Furthermore, we extend our heartfelt appreciation to our families (including Xiaoyue Cui, Muyuan Wang, Safura Tazeen, Khasim BI, Shirleen Chow, Adler Teoh, Hriday Bhoyar, Swati Kolkhede, and all) for their unwavering encouragement throughout the creation of this book. We dedicate this book to them. The first author, Zhiyuan Wang, would also like to convey special thanks and appreciation to his Ph.D. advisors, Prof. Zhe Wu, Prof. Xiaonan Wang, and Prof. Gade Pandu Rangaiah from the National University of Singapore. Although they were not involved in this book, Zhiyuan deeply cherishes their sincere and invaluable guidance in his Ph.D. journey, which has helped him become a better researcher and educator.

Despite our best efforts to ensure the accuracy of the content within this book, errors may inadvertently persist. If you come across any inaccuracies or omissions, we kindly request that you bring them to our attention by emailing us at [email protected]. We are committed to rectifying such oversights in future editions and will post corrections on our shared https://drive.google.com/drive/folders/1FqJvo4ZPazNbEH_GlHFoodqvegnQmHc n?usp=share_link

Zhiyuan Wang DigiPen Institute of Technology Singapore Singapore National University of Singapore SingaporeSayed Ameenuddin Irfan DigiPen Institute of Technology Singapore Singapore National University of Singapore SingaporeZhiyuan Wang DigiPen Institute of Technology Singapore SingaporeChristopher Teoh DigiPen Institute of Technology Singapore Singapore &Priyanka Hriday Bhoyar DigiPen Institute of Technology Singapore Singapore

Introduction to Machine Learning

Zhiyuan Wang,Sayed Ameenuddin Irfan,Christopher Teoh,Priyanka Hriday Bhoyar

Abstract

Machine learning, a rapidly growing subfield of computer science, has had a significant impact on many industries and our lives. This chapter discusses the brief history of machine learning, its widespread adoption as a de facto feature, and fundamental concepts such as supervised and unsupervised learning, regression and classification, and underfitting and overfitting. We also emphasize the importance of understanding machine learning through numerical examples, which can bridge the gap between abstract mathematical theories and practical applications of machine learning algorithms. By developing a strong foundation in machine learning, readers/students can harness its potential to address challenges and opportunities across diverse sectors.

Keywords: Numerical Examples, Machine Learning History, Supervised Learning, Unsupervised Learning, Regression, Classification, Underfitting, Overfitting.

1.1. BRIEF HISTORY OF MACHINE LEARNING

Machine learning is a subfield of computer science that involves the creation of algorithms that can learn from data and make predictions. It has a long and rich history [1], with roots dating back to the 1950s when the field of artificial intelligence was founded. This field focused on developing machines that could perform tasks that typically require human-like intelligence, such as recognizing patterns, learning from experience, and making decisions. The first machine learning algorithms were developed in the 1960s, including decision tree and nearest neighbor algorithms. The 1980s saw the rapid growth of the field with the development of algorithms such as artificial neural network and support vector machine. These algorithms were applied to a wide range of applications in the 1990s, including natural language processing, computer vision, and speech recognition. In the 2000s, the field continued to evolve with the development of new algorithms, such as gradient boosting, and the increasing use of machine learning in industries such as finance and healthcare. The 2010s saw the widespread adoption of machine learning, aided by the advent of big data and the development of powerful graphics processing units (GPU) that could be used to train large and complex machine learning models. The subfield of deep learning [2], which typically involves the use of multi-layered neural networks, became particularly popular and found application across a diverse range of domains. Today, machine learning is a rapidly growing field that is currently being applied in various sectors. It has the potential to revolutionize many industries and has already had a significant societal impact.

1.2. MACHINE LEARNING AS A DE FACTO FEATURE