Data Science and Machine Learning: Mathematical and Statistical Methods

Table of Contents Updated PDF (20 Mb) Original PDF Reviews About the Authors Bibtex Reference Errata Solutions (odd-numbered) Python code (GitHub)

D.P. Kroese, Z.I. Botev, T. Taimre, R. Vaisman. Data Science and Machine Learning: Mathematical and Statistical Methods, Chapman and Hall/CRC, Boca Raton, 2019.

Z.I. Botev, D.P. Kroese, T. Taimre. Data Science and Machine Learning: Mathematical and Statistical Methods, Second Edition, Chapman and Hall/CRC, Boca Raton, 2025.

The purpose of DSML 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

The second 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.