Datafits

A datafit defines the loss on the complete linear predictor, including the intercept. Matrix operations belong to the design. Loss values and derivatives use the same averaging convention.

Datafit	Response	Loss	Compatible solvers
Gaussian	One finite real response per observation	Averaged squared error	Coordinate descent for L1, proximal gradient, IRLS, hybrid for supported penalties
Binomial	Finite values in $[0,1]$	Averaged Bernoulli negative log likelihood	Proximal gradient, IRLS, hybrid for supported penalties
Multivariate Gaussian	Multiple finite response columns	Squared error, summed over responses and averaged over observations	Proximal gradient with AxisPenalty

All three fit unpenalized intercepts by default. Response dimensions must match nonempty training observations. Data and parameters are validated when losses are evaluated or models are fitted.

shrinkage::Datafit supplies loss evaluation. DifferentiableDatafit adds gradients and observation metadata. shrinkage::SmoothDatafit asserts convexity, and shrinkage::DiagonalHessianDatafit supplies exact, potentially signed second derivatives. QuadraticModelDatafit supplies nonnegative working curvature to IRLS. These capabilities determine which solvers can fit a composition.

Gaussian and binomial models also support configurable links through the typed Rust IRLS API using .with_link(...).