aom_preprocess — AOM (Adaptive Operator Mixture) preprocessing bank

Group: Diagnostic · Registry tolerance: 1e-08

Description

AOM preprocessing pipeline (§17 Phase 4)

Registry note — In-tree nirs4all.operators.models.sklearn.aom_pls is the sanctioned provider. pls4all currently exposes the preprocessing primitive, while nirs4all exposes the full AOM/POP estimator stack; parity is qualitative.

Parameters

Name

Type

Default

Notes

X

—

required

current public binding signature

y

—

None

current public binding signature

operators

—

None

current public binding signature

gating_mode

str | int

'soft'

current public binding signature

n_operators

int

3

registry benchmark cell value

Explanations

Bibliographic source

Beurier, G., Reiter, R., Noûs, C., Rouan, L. & Cornet, D. (2026). Reframing preprocessing selection as model-internal calibration in near-infrared spectroscopy: a large-scale benchmark of operator-adaptive PLS and Ridge models. arXiv:2605.13587. https://arxiv.org/abs/2605.13587 — introduces operator-adaptive PLS (AOM-PLS / POP-PLS) and the bench against 50+ NIRS datasets that the git-pinned oracle nirs4all.operators.models.sklearn.aom_pls is calibrated against.

Mathematical principle

aom_preprocess is the operator-bank primitive that AOM-PLS and POP-PLS build on. Given the centered spectral matrix \(\mathbf{X} \in \mathbb{R}^{n\times p}\) and a finite bank of strict-linear operators \(\{\mathbf{A}_b\}_{b=1}^{M} \subset \mathbb{R}^{p\times p}\) — matrices fully determined by the wavelength grid (identity, Savitzky–Golay smooth/derivative, finite difference, polynomial detrending, Norris–Williams, Whittaker; SNV / MSC / EMSC / ASLS / OSC are excluded because they depend on \(\mathbf{y}\) or on a reference spectrum) — aom_preprocess materializes the \(M\) preprocessed views \(\mathbf{X}_b = \mathbf{X}\mathbf{A}_b^{\top}\) and gates them.

Two gating modes are supported:

  • soft (\(\texttt{gating\_mode}=1\)): equal-weight average

\[\mathbf{X}_{\text{AOM}}^{\text{soft}} \;=\; \frac{1}{M}\sum_{b=1}^{M}\mathbf{X}\mathbf{A}_b^{\top}.\]

  • hard (\(\texttt{gating\_mode}=0\)): deterministic first-operator selection,

\[\mathbf{X}_{\text{AOM}}^{\text{hard}} \;=\; \mathbf{X}\mathbf{A}_{1}^{\top}.\]

Both modes preserve the cross-covariance identity exploited by the AOM/POP selectors: with \(\mathbf{S} = \mathbf{X}^{\top}\mathbf{Y}\) and any \(\mathbf{A}_b\) in the bank,

\[\bigl(\mathbf{X}\mathbf{A}_b^{\top}\bigr)^{\top}\mathbf{Y} \;=\; \mathbf{A}_b\,\mathbf{S},\]

so a downstream PLS step can score the whole bank by \(M\) cheap \(O(pq)\) left actions instead of \(M\) full \(O(np)\) matrix products. The motivation is that no single preprocessing is best on all calibrations — different wavelength regions favour different transforms — and the AOM-PLS / POP-PLS selectors exploit that by picking, respectively, a global operator (one \(b^{\star}\) for the whole model) or a per-component operator (one \(b_a\) for each latent direction). Predictions on new spectra reuse the absorbed operator(s) through the recovered original-space coefficients — no preprocessing replay at predict time.

Appropriate uses

Automated comparison of candidate spectral preprocessing chains under an explicit validation protocol.

Limits and validation

Searching many chains increases selection bias; every fitted transform and chain choice must be confined to training folds.

Implementation

n4m_model_selection_aom_preprocessing_fit. Reference: git-pinned oracle nirs4all.operators.models.sklearn.aom_pls (sanctioned exception).

Sources and provenance

Current implementation: cpp/src/core/aom_preprocessing.cpp.

API and bindings

C ABI (ABI 2): n4m_model_selection_aom_preprocessing_fit. Use the linked public header for the exact signature, configuration, and result handles.

Python (verified public re-export):

from n4m.model_selection.aom_search import aom_preprocess
result = aom_preprocess(X)

Source signature: aom_preprocess(X, y = None, *, operators = None, gating_mode: str | int = 'soft') (n4m/_impl/native.py).

R: no current source-verified entry point was found for this catalog method.

MATLAB / Octave: no current source-verified entry point was found for this catalog method.

Registry parity references 📐

  • 📐 nirs4all (python · python) — nirs4all in-tree · strict (rmse_rel ≤ 1e-08) — In-tree nirs4all AOM provider (sanctioned external reference). pls4all’s current primitive exposes a small operator-bank preprocessing kernel, while nirs4all exposes the full AOM/POP estimator stack; the parity remains qualitative.

Benchmarks

Archived measurement identity. Backend labels in this table are the raw IDs recorded when the benchmark ran (including historical pls4all.* IDs). They preserve measurement provenance and do not describe a current public Python, R, or MATLAB binding; use the source-verified API and bindings section above for current entry points.

Adaptive wall-clock per cell measured against full_matrix.csv. Only backends that implement this method are listed; libraries without the method are omitted.

Verdict  ·  ✓ ref / ≈ ref / ~ shape mark a reference-gate pass at strict / relaxed / qualitative tolerance  ·  ✓ bind = archived binding-harness result agrees with the C++ baseline  ·  ⇄ cross-check = documented by-design selector/RNG/model, noncanonical API/facade convention, or secondary oracle  ·  ✗ divergent  ·  ⚠ error  ·  — not run. The fastest backend per column is marked 🏆.

Reference gate: strict — numeric equivalence (rmse_rel_tol ≤ 1e-08).

Rows tagged with 📐 are the canonical parity references for this method (declared in parity_timing.registry). C++ and external rows show reference parity; archived language-harness rows show binding parity against the C++ backend. Hover the icon for role and tolerance band.

BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref1.85 ms
Python · archived pls4all benchmark
pls4all.python✓ bind1.76 ms
pls4all.sklearn✓ bind1.75 ms🏆
R · archived pls4all benchmark
pls4all.R✓ bind6.07 ms
pls4all.R.formula✓ bind7.96 ms
pls4all.R.mdatools✓ bind6.56 ms
pls4all.R.pls✓ bind7.33 ms
Python · external
📐nirs4allsource2.13 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref2.95 ms
Python · archived pls4all benchmark
pls4all.python✓ bind1.74 ms🏆
pls4all.sklearn✓ bind3.37 ms
R · archived pls4all benchmark
pls4all.R✓ bind10.4 ms
pls4all.R.formula✓ bind35.7 ms
pls4all.R.mdatools✓ bind29.5 ms
pls4all.R.pls✓ bind32.9 ms
Python · external
📐nirs4allsource11.5 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref3.32 ms
Python · archived pls4all benchmark
pls4all.python✓ bind7.59 ms
pls4all.sklearn✓ bind4.10 ms
R · archived pls4all benchmark
pls4all.R✓ bind9.94 ms
pls4all.R.formula✓ bind9.00 ms
pls4all.R.mdatools✓ bind8.97 ms
pls4all.R.pls✓ bind8.32 ms
Python · external
📐nirs4allsource1.87 ms🏆

See also: benchmark overview · methods index · interactive dashboard