recursive_pls — Recursive (moving-window) PLS

Group: Core PLS · Registry tolerance: 1e-08

Description

Recursive (moving-window) PLS

Parameters

Name	Type	Default	Notes
n_components	int	3	registry benchmark cell value
window_size	int	60	registry benchmark cell value

Explanations

Bibliographic source

Helland, K., Berntsen, H. E., Borgen, O. S. & Martens, H. (1992). Recursive algorithm for partial least squares regression. Chemometrics and Intelligent Laboratory Systems 14(1–3), 129–137. DOI 10.1016/0169-7439(92)80098-O.

Mathematical principle

Process-analytical instruments produce streams of spectra under drifting conditions (changing humidity, instrument warm-up, fouling). Recursive PLS maintains a fitted model that adapts as new samples arrive by re-fitting on a sliding window of the most recent \(w\) samples.

At time step \(t\), the model is fit on \(\{(\mathbf{x}_{t-w+1}, y_{t-w+1}), \ldots, (\mathbf{x}_t, y_t)\}\) and applied to incoming \(\mathbf{x}_{t+1}\). Computational cost is \(O(wpk)\) per step. The window width \(w\) controls a stability/adaptability trade-off: short windows track drift aggressively but are noisier; long windows are stable but lag.

More sophisticated recursive variants (Qin 1998) use exponential forgetting factors instead of a hard window. pls4all’s variant uses the hard-window form for deterministic parity with R pls rolling refits.

Appropriate uses

Updating a linear calibration as new batches arrive without retaining and refitting the complete historical data set.

Limits and validation

Forgetting-factor updates can drift or forget rare regimes; sample order and batch composition affect the result.

Implementation

n4m_estimators_recursive_pls_run (returns predictions only — no global coefficient export, since the model changes per step). The Python sklearn wrapper is an in-sample-only estimator.

Sources and provenance

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

API and bindings

C ABI (ABI 2): n4m_estimators_recursive_pls_run. Use the linked public header for the exact signature, configuration, and result handles.

Python: no current AST-verified public n4m re-export was found for this method. The linked C ABI above is the documented surface in this checkout.

R (source-verified): recursive_pls(formula, data, ncomp = 2L, window_size = 50L, na.action = stats::na.omit).

The source signature has additional required inputs, so no example call is fabricated.

MATLAB / Octave (source-verified): recursive_pls(X, Y, n_components, window_size).

The source signature has additional required inputs, so no example call is fabricated.

Registry parity references 📐

• 📐 ref.python_scikit_learn (python · python) — scikit-learn 1.4.2 · strict (rmse_rel ≤ 1e-08) — Moving-window refit using sklearn PLSRegression (NIPALS).

• 📐 ref.r_pls (R · r) — pls 2.8.5 · strict (rmse_rel ≤ 1e-08) — Moving-window refit using R pls::plsr (SIMPLS by default).

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.

1 thread

Backend	Parity	200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 9e-16	2.92 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	2.79 ms🏆
pls4all.sklearn	✓ bind	3.10 ms
R · archived pls4all benchmark
pls4all.R	✓ 4e-15	5.74 ms
pls4all.R.formula	✓ 4e-15	6.55 ms
pls4all.R.mdatools	✓ 4e-15	6.99 ms
pls4all.R.pls	✓ 4e-15	7.36 ms
Python · external
📐ref.python_scikit_learn	source	48.1 ms
R · external
📐ref.r_pls	⇄ +4e-15	141.6 ms

3 threads

Backend	Parity	200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 9e-16	2.87 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	2.94 ms
pls4all.sklearn	✓ bind	3.11 ms
R · archived pls4all benchmark
pls4all.R	✓ 4e-15	5.97 ms
pls4all.R.formula	✓ 4e-15	6.97 ms
pls4all.R.mdatools	✓ 4e-15	7.91 ms
pls4all.R.pls	✓ 4e-15	6.92 ms
Python · external
📐ref.python_scikit_learn	source	46.3 ms
R · external
📐ref.r_pls	⇄ +4e-15	144.8 ms

10 threads

Backend	Parity	200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 9e-16	2.95 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	3.02 ms
pls4all.sklearn	✓ bind	3.06 ms
R · archived pls4all benchmark
pls4all.R	✓ 4e-15	5.98 ms
pls4all.R.formula	✓ 4e-15	7.42 ms
pls4all.R.mdatools	✓ 4e-15	6.94 ms
pls4all.R.pls	✓ 4e-15	7.32 ms
Python · external
📐ref.python_scikit_learn	source	48.7 ms
R · external
📐ref.r_pls	⇄ +4e-15	147.3 ms

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See also: benchmark overview · methods index · interactive dashboard