Mathematical Pictures at a Data Science Exhibition
(Sprache: Englisch)
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...
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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.
Inhaltsverzeichnis zu „Mathematical Pictures at a Data Science Exhibition “
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.
Autoren-Porträt von Simon Foucart
Texas A & M University
Bibliographische Angaben
- Autor: Simon Foucart
- 2022, New edition, 350 Seiten, Masse: 15,2 x 22,9 cm, Taschenbuch, Englisch
- Verlag: Cambridge University Pr.
- ISBN-10: 100900185X
- ISBN-13: 9781009001854
Sprache:
Englisch
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