Author:
Foucart, Simon, author.
ImprintCambridge, United Kingdom ; New York, NY : Cambridge University Press, 2022.
Descriptionxx, 318 pages : illustrations ; 24 cm
Note:Part one. Machine Learning -- Rudiments of Statistical Learning -- Vapnik-Chervonenkis Dimension -- Learnability for Binary Classification -- Support Vector Machines -- Reproducing Kernel Hilbert -- Regression and Regularization -- Clustering -- Dimension Reduction -- Part two. Optimal Recovery -- Foundational Results of Optimal Recovery -- Approximability Models -- Ideal Selection of Observation Schemes -- Curse of Dimensionality -- Quasi-Monte Carlo Integration -- Part three. Compressive Sensing -- Sparse Recovery from Linear Observations -- The Complexity of Sparse Recovery -- Low-Rank Recovery from Linear Observations -- Sparse Recovery from One-Bit Observations -- Group Testing -- Part four. Optimization -- Basic Convex Optimization -- Snippets of Linear Programming -- Duality Theory and Practice --Semidefinite Programming in Action -- Instances of Nonconvex Optimization -- Part five. Neural Networks -- First Encounter with ReLU Networks -- Expressiveness of Shallow Networks -- Various Advantages of Depth -- Tidbits on Neural Network Training -- Appendix A. High-Dimensional Geometry -- Appendix B. Probability Theory -- Appendix C. Functional Analysis -- Appendix D. Matrix Analysis -- Appendix E. Approximation Theory.
Bibliography Note:Includes bibliographical references (pages 311-313) and index.
Note:"In the past few decades, heuristic methods adopted by big tech companies have complemented existing scientific disciplines to form the new field of Data Science. This text provides deep and comprehensive coverage of the mathematical theory supporting the field. Composed of 27 lecture-length chapters with exercises, it embarks the readers on an engaging itinerary through key subjects in data science, including machine learning, optimal recovery, compressive sensing (also known as compressed sensing), optimization, and neural networks. While standard material is covered, the book also includes distinctive presentations of topics such as reproducing kernel Hilbert spaces, spectral clustering, optimal recovery, compressive sensing, group testing, and applications of semidefinite programming. Students and data scientists with less mathematical background will appreciate the appendices that supply more details on some of the abstract concepts."-- Provided by publisher.
