Book map · Francis Bach
MIT Press, 2024.
StatsMLlib provides formal counterparts for mathematical preliminaries, linear least squares, empirical risk minimization, complexity control, and constrained sparse-regression arguments.
Coverage note. The map records material with a direct formal counterpart in StatsMLlib and does not imply complete formalization of any listed chapter.
Chapter-level overlap
The map follows the chapter organization of the published book.
Eigenvalue and singular-value tools, Hoeffding and McDiarmid inequalities, finite-maximal bounds, Gaussian and sub-Gaussian concentration, and random-matrix inequalities formalize much of the linear-algebra and probability background.
Least-squares definitions and the basic inequality, fixed-design geometry, a sharp finite-sample linear prediction rate, star-shaped localization, and the spectral foundations of PCA overlap with the chapter’s ordinary least-squares and dimension-reduction material.
Covering numbers, bounded differences, symmetrization, Rademacher complexity, uniform-deviation bounds, and ℓ¹- and ℓ²-constrained linear predictor classes formalize core tools for controlling estimation error.
The constrained least-squares framework, ℓ¹-bounded predictor and fixed-design classes, Maurey-type covering estimates, localized Gaussian complexity, critical radii, and resulting prediction-error bounds give a formal counterpart to the chapter’s constrained sparse-regression analysis.