Mastering Linear Algebra, Probability, and Statistics for Machine Learning and NLP

Natural language processing (NLP) and machine learning (ML) are two fields that have significantly benefited from mathematical concepts, particularly linear algebra and probability theory. These fundamental tools enable the analysis of the relationships between variables, forming the basis of many NLP and ML models. This chapter provides a comprehensive introduction to linear algebra and probability theory, including their practical applications in NLP and ML. The chapter commences with an overview of vectors and matrices and covers essential operations. Additionally, the basics of statistics, required for understanding the concepts and models in subsequent chapters, will be explained. Finally, the chapter introduces the fundamentals of optimization, which are critical for solving NLP problems and understanding the relationships between variables. By the end of this chapter, you will have a solid foundation...