Mathematical Pictures at a Data Science Exhibition
Mathematical Pictures at a Data Science Exhibition
$99.99
USDThis text provides deep and comprehensive coverage of the mathematical background for data science, including machine learning, optimal recovery, compressed sensing, optimization, and neural networks. 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 embarks the readers on an engaging itinerary through the theory supporting the field. Altogether, twenty-seven lecture-length chapters with exercises provide all the details necessary for a solid understanding of key topics in data science. While the book covers standard material on machine learning and optimization, it also includes distinctive presentations of topics such as reproducing kernel Hilbert spaces, spectral clustering, optimal recovery, compressed sensing, group testing, and applications of semidefinite programming. Students and data scientists with less mathematical background will appreciate the appendices that provide more background on some of the more abstract concepts.
- Specially designed for mathematicians and graduate students in mathematics who want to learn more about data science
- Presents a broad view of mathematical data science by including a wide variety of subjects, from the very popular subject of machine learning to the lesser-known subject of optimal recovery
- Proves at least one theoretical result in each chapter, helping the reader develop a sound understanding of topics explained with detailed arguments
- Includes original content that has never been published before in book form, such as the presentation of compressive sensing through a nonstandard restricted isometry property
- Provides background for some of the more abstract concepts in the appendices
- Author's GitHub page includes computational illustrations made in MATLAB and Python to demonstrate how the theory is applied
Reviews & endorsements
'What a great read and a unique perspective! It contains a beautifully written rigorous treatment of many areas of Mathematical Data Science - perfect for a graduate course or for scholars of related backgrounds. The presentation and 'walk through' of the topic are a great way to motivate its study.' Deanna Needell, University of California, Los Angeles
'The title perfectly captures the book's approach, and the author is a wonderful guide to this gallery. He sticks to the facts and gives a cogent yet thorough description of the most foundational mathematical results. The book will fill in some missing mathematical background for many of us working in data science, and the exercises make it an excellent class text as well.' Stephen Wright, University of Wisconsin - Madison
'With Mathematical Pictures at a Data Science Exhibition, Simon Foucart has deftly illuminated the mathematical side of data science with a rigorous yet accessible treatment. This book, like a good museum, will be a valuable resource for experts, students, and casual enthusiasts.' Richard Baraniuk, Rice University
'… an excellent discussion of representative algorithms as used in data science today - one of the best in-depth resources to appear in recent years for a scientist working on new analytic approaches or optimization … Highly recommended.' J. Brzezinski, Choice
Product details
April 2022Hardback
9781316518885
350 pages
235 × 158 × 21 mm
0.65kg
Not yet published - available from February 2025
Table of Contents
- Part I. Machine Learning:
- 1. Rudiments of Statistical Learning
- 2. Vapnik–Chervonenkis Dimension
- 3. Learnability for Binary Classification
- 4. Support Vector Machines
- 5. Reproducing Kernel Hilbert
- 6. Regression and Regularization
- 7. Clustering
- 8. Dimension Reduction
- Part II Optimal Recovery:
- 9. Foundational Results of Optimal Recovery
- 10. Approximability Models
- 11. Ideal Selection of Observation Schemes
- 12. Curse of Dimensionality
- 13. Quasi-Monte Carlo Integration
- Part III Compressive Sensing:
- 14. Sparse Recovery from Linear Observations
- 15. The Complexity of Sparse Recovery
- 16. Low-Rank Recovery from Linear Observations
- 17. Sparse Recovery from One-Bit Observations
- 18. Group Testing
- Part IV Optimization:
- 19. Basic Convex Optimization
- 20. Snippets of Linear Programming
- 21. Duality Theory and Practice
- 22. Semidefinite Programming in Action
- 23. Instances of Nonconvex Optimization
- Part V Neural Networks:
- 24. First Encounter with ReLU Networks
- 25. Expressiveness of Shallow Networks
- 26. Various Advantages of Depth
- 27. 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.
