Struct MultinomialFitOutputs 

pub struct MultinomialFitOutputs {
    pub coefficients_active: Array2<f64>,
    pub fitted_probabilities: Array2<f64>,
    pub iterations: usize,
    pub penalized_neg_log_likelihood: f64,
    pub deviance: f64,
    pub coefficient_covariance: Array2<f64>,
}

Outputs of fit_penalized_multinomial.

Fields

coefficients_active: Array2<f64>

Active-class coefficient block, shape (P, K-1) (column a is β_a). The reference class K - 1 has β_{K-1} ≡ 0 by construction and is not stored.

fitted_probabilities: Array2<f64>

Fitted probabilities, shape (N, K).

iterations: usize

Number of Newton iterations executed (including the final step that satisfied the tolerance). Non-convergence (outside the separation lane, which escalates to the Firth refit) is surfaced as the typed EstimationError::FixedLambdaNewtonDidNotConverge rather than an Ok with a flag, so every constructed value of this struct is a certified converged fit (SPEC: a fit only ever comes from a converged optimization).

penalized_neg_log_likelihood: f64

Penalized negative log-likelihood at the returned β̂: −log L(β̂) + ½ Σ_a λ_a · β̂_a^T S β̂_a.

deviance: f64

Unpenalized deviance −2 log L(β̂) for diagnostic reporting.

coefficient_covariance: Array2<f64>

Joint Laplace posterior coefficient covariance H⁻¹ at the converged β̂, shape (P·(K−1))×(P·(K−1)) (#1101). Block-ordered to match the stacked active-class coefficient vector β = [β_0; …; β_{K-2}]: active class a’s P coefficients occupy rows/cols a·P .. (a+1)·P, indexed θ[a·P + i] = β̂[i, a]. This is the Laplace covariance from the factored penalized Hessian XᵀWX + diag_a(λ_a)⊗S; it drives the delta-method per-class probability standard errors (Self::logistic_normal_softmax_moments) on the fixed-λ inner-solve path.

Implementations

impl MultinomialFitOutputs

pub fn n_active_classes(&self) -> usize

Number of active classes M = K − 1 (columns of Self::coefficients_active).

pub fn p_per_class(&self) -> usize

Per-class coefficient dimension P (rows of Self::coefficients_active).

pub fn logistic_normal_softmax_moments( &self, x_new: ArrayView2<'_, f64>, ) -> Result<(Array2<f64>, Array2<f64>), EstimationError>

Integrate the logistic-normal coefficient posterior at fresh design rows: E[softmax(η)] and its marginal standard deviations with η ~ N(x'β̂, x'Σx), the full joint covariance (cross-class blocks included) contracted into each row’s active-logit covariance before deterministic adaptive integration.

This is NOT the posterior mean, and the name says so on purpose (#2612)

The quantity a caller usually wants — the posterior mean probability — is not this. Integrating a nonlinear functional over the Laplace Gaussian keeps the curvature half of the O(n⁻¹) correction to a posterior mean and drops the skewness half; on a (quasi-)separated softmax the two are neither small nor same-signed, and the result is under-confident by up to tens of percentage points at unchanged argmax. The posterior mean is computed by crate::multinomial_predictive as a ratio of normalising constants, and MultinomialSavedModel::predict_probabilities is the entry point that publishes it.

What this function IS, and why it stays: the exact moments of softmax under a STATED Gaussian. That is a well-defined object with its own uses (propagating a declared coefficient uncertainty through the link, and pinning the integrator itself), and naming it for the Gaussian rather than for the posterior is what keeps the two from being confused again.

pub fn logistic_normal_softmax_moments_with_control( &self, x_new: ArrayView2<'_, f64>, control: &MultinomialPosteriorIntegrationControl, ) -> Result<(Array2<f64>, Array2<f64>), EstimationError>

Trait Implementations

impl Clone for MultinomialFitOutputs

fn clone(&self) -> MultinomialFitOutputs

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for MultinomialFitOutputs

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.