Book map · Martin J. Wainwright
A Non-Asymptotic Viewpoint (Cambridge University Press, 2019).
StatsMLlib overlaps with the book’s concentration, empirical-process, metric-entropy, random-matrix, sparse-regression, PCA, and localized least-squares developments.
Coverage note. The entries identify formalized overlap with whole chapters without implying that every theorem, estimator, or application in those chapters has been formalized.
Chapter-level overlap
The map follows the chapter organization of the published book.
Moment-generating-function methods, Chernoff and Hoeffding bounds, sub-Gaussian scales, finite maxima, Gaussian product measures, and Lipschitz Gaussian concentration cover the principal formalized topics.
Formalized functional methods include entropy and its variational duality, conditional decomposition and Han-type subadditivity, Efron–Stein, Bernoulli and Gaussian logarithmic Sobolev inequalities, Gaussian Poincaré, tensorization, and the resulting Gaussian concentration bounds.
Rademacher sign calculus and complexity, symmetrization, McDiarmid’s bounded-difference inequality, and expected and high-probability uniform-deviation bounds are developed for finite, countable, and separably indexed function classes.
Covering and packing numbers, Euclidean and ℓ¹ covering arguments, one-step discretization, finite-class maximal bounds, Massart’s lemma, Dudley and truncated Dudley integrals, and local Gaussian complexity connect metric entropy to empirical processes.
Singular-value and variational foundations support operator-norm bounds for independent sub-Gaussian entries, two-sided singular-value bounds for isotropic sub-Gaussian rows, covariance-deviation arguments, and matrix Bernstein via trace-MGF methods.
The formalized overlap consists of ℓ¹-constrained linear predictor classes, fixed-design geometry, Maurey-type covering estimates, and localized least-squares complexity and error bounds. These are foundations for sparse regression rather than a formalization of every estimator in the chapter.
Spectral and Rayleigh-quotient characterizations, singular values, Courant–Fischer, Eckart–Young–Mirsky, Weyl inequalities, and Davis–Kahan perturbation bounds formalize the deterministic matrix foundations of PCA.
Least-squares estimators and their basic inequality, star-shaped localization, critical radii, local Gaussian complexity, master error bounds, the sharp finite-sample linear rate, and ℓ¹-constrained applications formalize the chapter’s central localization pipeline.
Monotonicity of localized empirical and Gaussian processes, critical-radius machinery, covering-based local complexity, and uniform deviation control provide the formalized basis for localized uniform laws.