gamrs 0.1.0a2

GAM core (Rust) with sklearn-style Python bindings — alpha

gamrs

Generalised Additive Models in Rust — a clean-room reimplementation built on six composable trait layers (Basis, BasisTransform, Loss/Link/VarianceFn, InnerSolver, ScoreDerivatives, OuterSolver). Designed for parity with R's mgcv and the sibling mgcv_rust crate.

Status: alpha. Multi-smooth additive (y ~ s(x0) + s(x1)) and tensor products (te(x0, x1)) both ship in this release — the latter leap-frogs mgcv_rust. Shape-aware families (scat, NegBin, Tweedie, Ocat, ELF) are still single-smooth-only; production users with multi-smooth shape-aware models should stay on mgcv-rust for now.

What's in this alpha

Families (all 1-D parity, 10 families)

Family	Link	Inner solver	Outer Newton	Parity (μ rel-err)
Gaussian	identity	one-Cholesky	1-D Newton	~3e-6
Bernoulli	logit	PIRLS	1-D Newton	~1e-3
Poisson	log	PIRLS	1-D Newton	~8e-5
QuasiPoisson	log	PIRLS	1-D Newton (prof φ)	~2e-4
QuasiBinomial	logit	PIRLS	1-D Newton (prof φ)	~7e-5
Gamma	log	PIRLS	1-D Newton (prof φ)	~2e-2
InverseGaussian	log	PIRLS	1-D Newton (prof φ)	~3e-4
NegBin	log	PIRLS	2-D joint Newton	~9e-7
Tweedie	log	PIRLS	3-D joint Newton	~2e-1
TDist (scat)	identity	PIRLS	3-D joint Newton	~2e-2
Ocat	logit	gam.fit5	joint β + threshold	smoke
Quantile (ELF)	identity	Armijo BT	1-D Newton	smoke

Bases

• Cr — cubic regression splines (default for 1-D smooths)
• Re — random effects (bs="re")
• Tensor<A, B> — anisotropic tensor product (te(x0, x1))

Smooth strategies

• Single 1-D smooth — y ~ s(x0)
• Additive multi-smooth — y ~ s(x0) + s(x1) + s(x2) (parity with mgcv_rust on Gaussian/Bernoulli/Poisson/Gamma/InvGauss/QuasiPoisson/QuasiBinomial)
• Tensor product — y ~ te(x0, x1) (leap-frogs mgcv_rust; v0.x doesn't have this)

Python API

PyO3 bindings + numpy. sklearn-like with vcov, predict_ci, predict_diff, serialize/deserialize, GamPredictor for inference-only deployment.

Not in this alpha (follow-ups)

• Multi-smooth shape-aware families — scat/TDist, NegBin, Tweedie, Ocat, ELF/quantile gated at single-smooth via runtime error. Lifting θ packing from [ρ, shape…] to [ρ_0, …, ρ_{T-1}, shape…] is tracked.
• s(x0, x1) TPRS — isotropic thin-plate; separate basis kind from te().
• 3+ margin tensor products te(x0, x1, x2) — mechanical generalization.
• ti(x0, x1) centred tensor interaction — needs main-effect orthogonalisation.

Use (Rust)

use gamrs::{TermSpec, MarginKind, DesignStrategy};
use ndarray::Array2;

let x: Array2<f64> = /* (n, n_input_dims) */;
let y = /* Array1<f64> */;

// Single 1-D smooth
let fit = gamrs::fit(gamrs::family::gaussian_identity(), x.view(), y.view(), None, 10)?;

// Multi-smooth additive
let fit = gamrs::fit_with_design(
    gamrs::family::gaussian_identity(),
    DesignStrategy::Additive { terms: vec![
        TermSpec::Cr { col: 0, k: 10 },
        TermSpec::Cr { col: 1, k: 15 },
    ]},
    x.view(), y.view(), None,
)?;

// Tensor product
let fit = gamrs::fit_with_design(
    gamrs::family::gaussian_identity(),
    DesignStrategy::Additive { terms: vec![
        TermSpec::Tensor { col_a: 0, col_b: 1, k_a: 5, k_b: 5, bs_a: MarginKind::Cr, bs_b: MarginKind::Cr },
    ]},
    x.view(), y.view(), None,
)?;

let mu = fit.predict(x.view())?;

Use (Python)

from gamrs import Gam, CrTerm, ReTerm, TeTerm

# Additive multi-smooth
g = Gam(terms=[CrTerm("x0", k=10), CrTerm("x1", k=15)])
g.fit(df, "y")
mu = g.predict(df)

# Tensor product
g = Gam(terms=[TeTerm(cols=("x0", "x1"), k=(5, 5))])
g.fit(df, "y")

Architecture

See architecture-assumptions.md in the repo root and the v2 plan note in ~/ObsidianVault/Projects/mgcv_rust/plans/mgcv_rust - v2 Architecture Plan 2026-05-22.md.

The trait layering (src/traits.rs):

Layer 1   Basis              ←  CrBasis, RandomEffectsBasis, TensorProductBasis<A, B>
Layer 1.5 BasisTransform     ←  SumToZero, StableReparam
Layer 2   Loss/Link/Variance ←  10 families (see table above)
Layer 3   InnerSolver        ←  GaussianClosedFormInner, PirlsInner, GamFit5Inner, ArmijoInner
Layer 4   ScoreDerivatives   ←  EnvelopeScore, ShapeAwareEnvelopeScore
Layer 5   OuterSolver        ←  NewtonWithHalving (ρ-dim generic)
Layer 6   FittedGam          ←  predict, predict_ci, predict_diff, vcov, serialize

Versioning

0.1.0-alpha.x indicates pre-stable. Breaking changes are expected on every minor bump until shape-aware multi-smooth lands.

License

MIT.