Book map · Mohri · Rostamizadeh · Talwalkar
2nd ed. (MIT Press, 2018).
StatsMLlib formalizes core tools behind Rademacher generalization bounds and connects them to finite-sample regression, spectral foundations for PCA, and concentration inequalities.
Coverage note. Each entry summarizes formalized overlap with a chapter or appendix; it does not assert complete formalization of that material.
Chapter-level overlap
The map follows the chapter organization of the second edition.
The Rademacher-complexity portion is formalized through empirical and expected complexity, finite sign-vector calculus, symmetrization, expected and high-probability uniform-deviation bounds, Massart’s finite-class lemma, Dudley chaining, and ℓ¹- and ℓ²-bounded linear predictor classes.
Formalized regression material includes least-squares estimators, the basic inequality, finite-sample guarantees for linear regression, ℓ¹-constrained regression classes, and Rademacher and localization tools for controlling prediction error.
Singular values, Courant–Fischer, Eckart–Young–Mirsky, Weyl inequalities, and Davis–Kahan perturbation bounds provide the formal spectral foundations for principal component analysis.
Hoeffding and Chernoff bounds, McDiarmid’s inequality, maximal inequalities, sub-Gaussian variables and processes, and Gaussian concentration formalize a substantial part of the appendix’s probability toolkit.