ML

Standalone, causal-free supervised-learning library: basic regression methods (linear least squares and series/sieve, ridge, lasso, logistic, generic ERM, kernel ridge, feedforward networks, random forests) as first-class objects, each with its defining-optimization, closed-form/structure, and population-target properties. Built on a dual-view spine (a parametric predictor and an extensional hypothesis class joined by a bridge). Imports nothing from the causal layers.

Core 29 core · 17 supporting · 8 submodules Roll-up of the causal-free machine-learning spine: losses, parametrized predictors and extensional hypothesis classes, empirical/population risk, the ERM-minimizer predicates, the parametric↔extensional bridge, the conve Kernel 14 core · 8 supporting · 7 submodules Roll-up: the abstract RKHS interface, kernel Gram matrices with regularized positive definiteness, the kernel-ridge representer theorem, the Rademacher complexity rate for the L²-ball linear class, and the genuine square Linear 7 core · 3 supporting · 3 submodules Roll-up of the linear-in-features regression family: ordinary least squares and ridge, including finite-sample optimization, closed-form normal-equation solutions, and population-risk target results. Binary 9 core · 6 supporting · 3 submodules Roll-up of the logistic part of Causalean.ML: convexity and compact-set existence for empirical logistic risk, pointwise Fisher consistency of the Bernoulli cross-entropy loss, and the root-n L² estimation rate for an L² Causal­Application 8 core · 2 supporting · 4 submodules This roll-up is the causal-application layer for Causalean.ML, kept separate from the causal-free core. Lasso 10 core · 3 supporting · 4 submodules Roll-up of the lasso family: l1penalty, lassoObjective, convexity of the finite objective, the scalar soft-thresholding optimality theorem softThreshold_isMinOn, and the Rademacher-complexity and squared-loss excess-risk Margin 1 core · 0 supporting · 1 submodule Roll-up: the Rademacher excess-risk rate for empirical minimization of a Lipschitz margin surrogate φ(y·⟪w,x⟩) over the W-ball of linear classifiers. Neural­Net 7 core · 1 supporting · 2 submodules Roll-up for dense affine layers, activations carrying Lipschitz constants, and uniform-width feedforward network evaluation. Ridge 14 core · 9 supporting · 4 submodules Ridge (L²-penalized) regression: the penalized least-squares objective and its normal equations (XᵀX + λI)β̂ = Xᵀy, the closed-form solution β̂ = (XᵀX + λI)⁻¹Xᵀy for λ > 0 (no full-rank assumption on X needed), the shrunk population target, and the root-n L² estimation rate of the sample ridge predictor toward that target (the learning-theory result the causal layer uses to discharge the DML nuisance-rate condition). Surrogate 7 core · 3 supporting · 2 submodules Surrogate-loss learning: generic convex empirical risk minimization with proper binary losses — losses whose conditional risk is minimized at the true probability — and their Fisher consistency (the population-risk minimizer recovers E[Y∣X]). Tree 6 core · 0 supporting · 2 submodules Roll-up: finite-partition (piecewise-constant) tree predictors and random-forest averaging, with the structural range-preservation property.