Mathematical Pictures at a Data Science Exhibition
$46.99 (P)
- Author: Simon Foucart, Texas A & M University
- Date Published: April 2022
- availability: Available
- format: Paperback
- isbn: 9781009001854
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This 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.
Read more- 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
See more reviews‘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
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×Product details
- Date Published: April 2022
- format: Paperback
- isbn: 9781009001854
- length: 350 pages
- dimensions: 228 x 151 x 17 mm
- weight: 0.51kg
- availability: Available
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.-
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Mathematical Pictures at a Data Science Exhibition
Simon Foucart
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