Probability and Statistics for Machine Learning - A Textbook

This book covers probability and statistics from the machine learning perspective. 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.Table of ContentChapter. 1. Probability and Statistics: An Introduction.- Chapter. 2. Summarizing and Visualizing Data.- Chapter. 3. Probability Basics and Random Variables.- Chapter. 4. Probability Distributions.- Chapter. 5. Hypothesis Testing and Confidence Intervals.- Chapter. 6. Reconstructing Probability Distributions from Data.- Chapter. 7. Regression.- Chapter. 8. Classification: A Probabilistic View.- Chapter. 9. Unsupervised Learning: A Probabilistic View.- Chapter. 10. Discrete State Markov Processes.- Chapter. 11. Probabilistic Inequalities and Extreme Value Analysis.- Bibliography.- Index.Biographical NoteCharu C. Aggarwal is a Distinguished Research Staff Member (DRSM) at the IBM T. J. Watson Research Center in Yorktown Heights, New York. He completed his undergraduate degree in Computer Science from the Indian Institute of Technology at Kanpur in 1993 and his Ph.D. in Operations Research from the Massachusetts Institute of Technology in 1996. He has published more than 400 papers in refereed conferences and journals, and has applied for or been granted more than 80 patents. He is author or editor of 20 books, including textbooks on linear algebra, machine learning, neural networks, and outlier analysis. Because of the commercial value of his patents, he has thrice been designated a Master Inventor at IBM. He has received several awards, including the EDBT Test-of-Time Award (2014), the ACM SIGKDD Innovation Award (2019), the IEEE ICDM Research Contributions Award (2015), and the IIT Kanpur Distinguished Alumnus Award (2023).He is also a recipient of the W. Wallace McDowell Award, the highest award given solely by the IEEE Computer Society across the field of computer science. He has served as an editor-in-chief of ACM Books and is currently serving as an editor-in-chief of the ACM Transactions on Knowledge Discovery from Data. He is a fellow of the SIAM, ACM, and the IEEE, for“contributions to knowledge discovery and data mining algorithms.”This book covers probability and statistics from the machine learning perspective. 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.Simple and intuitive discussions of probability and statistics Discusses details of applications of mathematical concepts to machine learning Provides mathematical details without losing the reader in complexity