Data Science and Machine Learning

Mathematical and Statistical Methods, Second Edition

Zdravko Botev, Dirk P. Kroese, Thomas Taimre

• Publisher: Chapman and Hall/CRC
• Year: 2025
• eBook ISBN: 9781040741535
• Topic: Economics
• Subtopic: Computer Science General
• Index: Economics

Praise for the first edition:

"In nine succinct but information-packed chapters, the authors provide a logically structured and robust introduction to the mathematical and statistical methods underpinning the still-evolving field of AI and data science."

- Joacim Rocklöv and Albert A. Gayle, International Journal of Epidemiology, Volume 49, Issue 6

"This book organizes the algorithms clearly and cleverly. The way the Python code was written follows the algorithm closely—very useful for readers who wish to understand the rationale and flow of the background knowledge."

- Yin-Ju Lai and Chuhsing Kate Hsiao, Biometrics, Volume 77, Issue 4

The purpose of Data Science and Machine Learning: Mathematical and Statistical Methods is to provide an accessible, yet comprehensive textbook intended for students interested in gaining a better understanding of the mathematics and statistics that underpin the rich variety of ideas and machine learning algorithms in data science.

New in the Second Edition

This expanded edition provides updates across key areas of statistical learning:

• Monte Carlo Methods: A new section introducing regenerative rejection sampling - a simpler alternative to MCMC.
• Unsupervised Learning: Inclusion of two multidimensional diffusion kernel density estimators, as well as the bandwidth perturbation matching method for the optimal data-driven bandwidth selection.
• Regression: New automatic bandwidth selection for local linear regression.
• Feature Selection and Shrinkage: A new chapter introducing the klimax method for model selection in high-dimensions.
• Reinforcement Learning: A new chapter on contemporary topics such as policy iteration, temporal difference learning, and policy gradient methods, all complete with Python code.
• Appendices: Expanded treatment of linear algebra, functional analysis, and optimization that includes the coordinate-descent method and the novel Majorization–Minimization method for constrained optimization.

Key Features:

• Focuses on mathematical understanding.
• Presentation is self-contained, accessible, and comprehensive.
• Extensive list of exercises and worked-out examples.
• Many concrete algorithms with Python code.
• Full color throughout and extensive indexing.
• A single-counter consecutive numbering of all theorems, definitions, equations, etc., for easier text searches.

Table of contents

• Cover Page
• Half Title page
• Series page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Notation
• Chapter 1 Importing, Summarizing, and Visualizing Data
• Chapter 2 Statistical Learning
• Chapter 3 Monte Carlo Methods
• Chapter 4 Unsupervised Learning
• Chapter 5 Regression
• Chapter 6 Feature Selection and Shrinkage
• Chapter 7 Reproducing Kernel Methods
• Chapter 8 Classification
• Chapter 9 Decision Trees and Ensemble Methods
• Chapter 10 Deep Learning
• Chapter 11 Reinforcement Learning
• Appendix A: Linear Algebra
• Appendix B: Functional Analysis
• Appendix C: Multivariate Differentiation and Optimization
• Appendix D: Probability and Statistics
• Appendix E: Python Primer
• Bibliography
• Index