دانلود کتاب جبر خطی، علوم داده و یادگیری ماشین

The purpose of this text is to provide a self-contained and mathematically rigorous intro- duction to modern methods of machine learning and data analysis at the advanced under- graduate/beginning graduate student level. The underlying mathematics — linear algebra, optimization, elementary probability and statistics, graph theory — is developed in detail with a minimum of prerequisites, relying only on very basic calculus, as described below. The book takes a mathematical approach to the subject, with a focus on understanding how algorithms work, using a range of linear algebraic tools, that are presented ab initio, combined with some elementary differential calculus, the latter primarily applied to opti- mization. In particular, this is not a book on statistical machine learning, and we do not make heavy use of probabilistic concepts or interpretations (although probability does make several appearances). We have done this in an effort to make the book accessible to as broad a range of readers and students as possible, while still providing mathematical depth to the material we have chosen to cover. While the overarching goal is to introduce readers to a broad range of modern machine learning methods and algorithms, enabling them to apply such techniques to real-world prob- lems, we do not shy away from stating theorems and writing out proofs, especially when they lead to insight into the underlying mathematics and an understanding as to when algorithms work well and when they work suboptimally, if not fail outright. In our approach, applications go hand in hand with theory, each reinforcing and inspiring the other. In this way, the reader will be well prepared when confronting recalcitrant practical problems, as well as being able to understand, or even actively contribute to, future developments in the field. The first five chapters develop, from the ground up, a broad range of ideas and techniques com- ing from linear algebra — meaning the theory and application of vectors and matrices — in a concrete and comprehensive form for direct use in data science and machine learning. These materials are inspired by the second author’s text, Applied Linear Algebra [181], coauthored with his wife, Chehrzad Shakiban. While there is some overlap in the exposition and the selection of examples and exercises, the material has been extensively rearranged and rewrit- ten. Indeed, this book takes an unusual and, in many ways, unique approach to introductory linear algebra that differs substantially from all existing introductory texts, including [181]. It begins with real vectors, reviewing their basic properties, including a detailed development of the key tools of the trade: bases, inner products, norms, and orthogonality, with a par- ticular emphasis on the utility of orthonormal bases. Matrices appear afterwards, building on their interrelationships with vectors and linear algebraic systems of equations. However, the standard solution method for linear systems, namely Gaussian elimination, is not covered.