Struct MeasureJetBasisSpec 

pub struct MeasureJetBasisSpec {
    pub center_strategy: CenterStrategy,
    pub order_s: f64,
    pub alpha: f64,
    pub tau0: f64,
    pub num_scales: usize,
    pub length_scale: f64,
    pub double_penalty: bool,
    pub learn_length_scale: bool,
    pub multiscale: bool,
    pub identifiability: MeasureJetIdentifiability,
    pub frozen_quadrature: Option<MeasureJetFrozenQuadrature>,
}

Measure-jet smooth configuration (mjs(x0, …, xd)).

The feature columns are ambient coordinates of data concentrated near an unknown low-dimensional (possibly stratified) set; the term learns the geometry from the empirical measure itself — centers as quadrature nodes, masses as μ-weights, local jet residuals as the roughness carrier — with no graph, mesh, or neighbor-set inside the statistical object.

Fields

center_strategy: CenterStrategy

Center/knot selection strategy (deterministic; quadrature of μ).

order_s: f64

Continuous smoothness order s ∈ (0, 2); 0.0 sentinel = auto (MEASURE_JET_DEFAULT_ORDER_S).

alpha: f64

Density-normalization exponent α (outer weight q^{1−2α}).

tau0: f64

Historical τ coordinate retained for frozen specs and ψ layout. The measure-jet energy itself uses the exact weighted affine projection and is independent of τ; the τ ψ derivatives are therefore zero.

num_scales: usize

Number of scale nodes; 0 sentinel = auto dyadic band.

length_scale: f64

Representer (Gaussian RBF) range ℓ; 0.0 sentinel = auto (median nearest-center spacing × MEASURE_JET_AUTO_LENGTH_SCALE_FACTOR).

double_penalty: bool

Add a separate function-space affine/null-component penalty alongside the jet-energy penalty. Its strength is independently REML-selected.

learn_length_scale: bool

REML-select the representer range ℓ as a design-moving outer dial, mirroring Matérn’s log_kappa. Default true — ℓ is a basis coordinate of the same kind as the Matérn κ, not a smoothing parameter, and a fitted model must choose it.

Why it cannot be a frozen geometric value (#2761)

The Gaussian kernel is strictly PD for every ℓ > 0, so ℓ does NOT change the basis rank (always m centers) — but it changes WHICH m-dim subspace the representers span. λ can only shrink inside a span; it cannot move one. So a mis-set ℓ is an error no smoothing parameter can repair, and the size of that error is not small. Measured on measure_jet_perf_parity’s 1-D-curve-in-3-D Gaussian fixture (n = 1500, σ = 0.10, 16 centers, p = 15), where span floor is the least-squares projection residual of the NOISELESS truth onto the realized design’s column span — the bound no λ can beat:

  arm                       ell      edf   span floor  unpen. LS  held-out
  frozen (auto ell)      0.5144   14.684    0.152488   0.155484   0.155584
  REML-selected ell      3.8813   14.006    0.000014   0.008155   0.009642
  matern(k=16)                -   14.619    0.006077   0.011989   0.011639
  duchon(k=16)                -   15.016    0.002443   0.011308   0.010521

At the frozen range the fit is already at edf/p = 0.98 and its held-out RMSE is the span floor: unpenalized least squares on the same design gives 0.1555, and dropping the null-component penalty moves the fourth decimal. Freeing ℓ drops the floor by four orders and the held-out RMSE by 16x, past both comparators, at LOWER edf — nothing is traded for it.

History (so a fourth flip needs new evidence)

299c83ffc (#1116) introduced this dial default-ON precisely to remove this fixture’s 13x. a3afd17a2 then found the one place it is unsafe — a BMS fit shares ONE mjs basis between the marginal mean and the log-slope surface, and a design-moving kernel scale on shared covariates is an identifiability hazard that reached a separation runaway — and contained it AT THE BMS ENTRY POINT with crate::smooth::freeze_measure_jet_length_scale_learning, which is still what runs there. b1d94d1a5 (#1041) nevertheless flipped the GLOBAL default off, and the 13x returned as #2761. The scoped freeze is the correct containment; the global one buys nothing it does not already buy and costs every single-surface fit its span alignment.

false freezes ℓ at the auto (or explicit) value with no outer enrollment. The term builder selects that automatically when the user pins length_scale= — an explicit range is a request, not a seed — mirroring the Matérn all_spatial_terms_kappa_fixed short-circuit.

multiscale: bool

Explicit opt-in for multiscale mode: the per-scale spectral penalty split plus the (α, ln τ) outer ψ dials. false (default) keeps the energy in single-scale mode at ANY center count. The separate double_penalty null component is available in both modes. There is no center-count auto-gate; the user opts in via mjs(…, multiscale=true). Persisted on the spec so freeze→replay enters the same mode.

identifiability: MeasureJetIdentifiability

Realized-design identifiability policy (see type docs).

frozen_quadrature: Option<MeasureJetFrozenQuadrature>

Fit-time quadrature replay (see type docs). None at fit time; Some on the frozen predict/ψ-trial path.

Trait Implementations

impl Clone for MeasureJetBasisSpec

fn clone(&self) -> MeasureJetBasisSpec

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for MeasureJetBasisSpec

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

Formats the value using the given formatter.

impl Default for MeasureJetBasisSpec

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for MeasureJetBasisSpec

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Serialize for MeasureJetBasisSpec

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.