Simon Foucart (Texas A & M University)

Mathematical Pictures at a Data Science Exhibition

• Broschiertes Buch

Produktbeschreibung

This text explores a diverse set of data science topics through a mathematical lens, helping mathematicians become acquainted with data science in general, and machine learning, optimal recovery, compressive sensing, optimization, and neural networks in particular. It will also be valuable to data scientists seeking mathematical sophistication.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 340
• Erscheinungstermin: 29. März 2022
• Englisch
• Abmessung: 229mm x 152mm x 19mm
• Gewicht: 506g
• ISBN-13: 9781009001854
• ISBN-10: 100900185X
• Artikelnr.: 63264562

Autorenporträt

Simon Foucart is Professor of Mathematics at Texas A&M University, where he was named Presidential Impact Fellow in 2019. He has previously written, together with Holger Rauhut, the influential book A Mathematical Introduction to Compressive Sensing (2013).

Inhaltsangabe

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.