High-Dimensional Probability : An Introduction with Applications in Data Science (Hardcover)

Preface; Appetizer: using probability to cover a geometric set; 1. Preliminaries on random variables; 2. Concentration of sums of independent random variables; 3. Random vectors in high dimensions; 4. Random matrices; 5. Concentration without independence; 6. Quadratic forms, symmetrization and contraction; 7. Random processes; 8. Chaining; 9. Deviations of random matrices and geometric consequences; 10. Sparse recovery; 11. Dvoretzky-Milman's theorem; Bibliography; Index.