Zdravko Botev - Böcker

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 4The 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 EditionThis 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.

An Advanced Course in Probability and Stochastic Processes provides a modern and rigorous treatment of probability theory and stochastic processes at an upper undergraduate and graduate level. Starting with the foundations of measure theory, this book introduces the key concepts of probability theory in an accessible way, providing full proofs and extensive examples and illustrations. Fundamental stochastic processes such as Gaussian processes, Poisson random measures, Lévy processes, Markov processes, and Itô processes are presented and explored in considerable depth, showcasing their many interconnections. Special attention is paid to martingales and the Wiener process and their central role in the treatment of stochastic integrals and stochastic calculus. This book includes many exercises, designed to test and challenge the reader and expand their skillset. An Advanced Course in Probability and Stochastic Processes is meant for students and researchers who have a solid mathematical background and who have had prior exposure to elementary probability and stochastic processes.Key Features:Focus on mathematical understandingRigorous and self-contained Accessible and comprehensiveHigh-quality illustrationsIncludes essential simulation algorithmsExtensive list of exercises and worked-out examplesElegant and consistent notation

This book celebrates the career of Pierre L’Ecuyer on the occasion of his 70th birthday. The Festschrift features article from the domains of Monte Carlo and quasi-Monte Carlo methods, Markov chains, sampling and low discrepancy sequences, simulation, rare events, graphics, finance, machine learning, stochastic processes, and tractability.