Название: Probability and Statistics for Machine Learning: A Textbook
Автор: Charu C. Aggarwal
Издательство: Springer
Год: 2024
Страниц: 530
Язык: английский
Формат: pdf (true), epub
Размер: 41.5 MB

This book covers probability and statistics from the Machine Learning perspective.

Most of Machine Learning is directly or indirectly related to probability and statistics. After all, Machine Learning is all about making predictions based on data, which inevitably leads to statistical methods. These statistical methods are often couched as models, which use probabilities to quantify the likelihoods of events. Therefore, having a strong background in probability and statistics is critical.

The familiarity required with probability and statistics often goes well beyond what is taught in undergraduate curricula. As a result, this presents a challenge to beginners in the field. In many cases, the type of techniques required from probability and statistics are specific to Machine Learning, which is not covered by generic courses on probability and statistics. This book therefore develops a treatment of probability and statistics from the specific perspective of Machine Learning.

This book teaches probability and statistics with a specific focus on Machine Learning applications. As a natural consequence of this approach, many key concepts in Machine Learning are covered in detail. Therefore, it is possible to learn a significant amount of Machine Learning while learning probability and statistics from this book.

The chapters of this book belong to three categories:

1. The basics of probability and statistics: These chapters focus on the basics of probability and statistics, and cover the key principles of these topics. Chapter 1 provides an overview of the area of probability and statistics as well as its relationship to Machine Learning. The fundamentals of probability and statistics are covered in Chapters 2 through 5.

2. From probability to Machine Learning: Many Machine Learning applications are addressed using probabilistic models, whose parameters are then learned in a data-driven manner. Chapters 6 through 9 explore how different models from probability and statistics are applied to Machine Learning. Perhaps the most important tool that bridges the gap from data to probability is maximum-likelihood estimation, which is a foundational concept from the perspective of Machine Learning. This concept is explored repeatedly in these chapters.

3. Advanced topics: Chapter 10 is devoted to discrete-state Markov processes. It explores the application of probability and statistics to a temporal and sequential setting, although the applications extend to more complex settings such as graphical data. Chapter 11 covers a number of probabilistic inequalities and approximations.

The style of writing promotes the learning of probability and statistics simultaneously with a probabilistic perspective on the modeling of Machine Learning applications. The book contains over 200 worked examples in order to elucidate key concepts. Exercises are included both within the text of the chapters and at the end of the chapters. The book is written for a broad audience, including graduate students, researchers, and practitioners.