# `recursive_pls` — Recursive (moving-window) PLS _Group_: **Core PLS** · _Registry tolerance_: `1e-08` ## Description Recursive (moving-window) PLS From the `pls4all.sklearn.RecursivePLSRegression` docstring: > Moving-window recursive PLS. ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `n_components` | `int` | `2` | Number of latent components extracted (k). | | `window_size` | `int` | `50` | Length of the moving window for recursive / interval-random-frog models. | ## 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. ### 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. ### 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. R roxygen note (`sklearn_extra.R::recursive_pls`): > Recursive PLS — formula entry point. MATLAB header (`bindings/matlab/+pls4all/RecursivePlsRegression.m`): ```text pls4all.RecursivePlsRegression Moving-window recursive PLS. In-sample only: result holds in-window predictions; no global coefficient matrix. `predict(X)` returns the stored predictions for the training X (length-preserved; warmup samples are 0). ``` ### Usage Every pls4all binding tab dispatches into the same C kernel; the external libraries listed at the bottom of the page are the parity references registered in `benchmarks.parity_timing.registry`. Switch tabs to read the same fit in your language. The R package now ships drop-in-compatible facades for the CRAN `pls` package (`plsr`, `pcr`, `mvr`) and for the `mdatools::pls(x, y, ...)` matrix idiom — those tabs appear only on the methods that have a meaningful equivalence. **pls4all bindings** ::::{tab-set} :class: pls4all-bindings :::{tab-item} C ABI · libn4m :sync: c :class-label: lang-c ```c /* C ABI — libn4m */ n4m_context_t* ctx = n4m_context_create(); n4m_config_t* cfg = n4m_config_create(); n4m_method_result_t* res = NULL; n4m_estimators_recursive_pls_run(ctx, cfg, &x_view, &y_view, /* hyperparams */, &res); /* … read coefficients / mask / scores via */ /* n4m_method_result_get_double_matrix / vector / scalar … */ n4m_method_result_destroy(res); n4m_config_destroy(cfg); n4m_context_destroy(ctx); ``` ::: :::{tab-item} Python · pls4all (raw) :sync: python-raw :class-label: lang-python ```python import pls4all from pls4all._methods import recursive_pls_run with pls4all.Context() as ctx, pls4all.Config() as cfg: res = recursive_pls_run(ctx, cfg, X, y, n_components=3) # then: res.matrix("predictions"), res.matrix("coefficients"), # res.vector("mask"), res.scalar("intercept"), … ``` ::: :::{tab-item} Python · pls4all.sklearn :sync: python-sklearn :class-label: lang-python ```python from pls4all.sklearn import RecursivePLSRegression mdl = RecursivePLSRegression(n_components=2, window_size=50) mdl.fit(X, y) y_hat = mdl.predict(X_test) ``` ::: :::{tab-item} R · pls4all_method() :sync: r-dispatcher :class-label: lang-r ```r library(pls4all) # Unified low-level dispatcher (May 2026 R cleanup): res <- pls4all_method("recursive_pls", X, y, n_components = 3L, params = list(window_size = 60L)) # res is a named list with MethodResult arrays/scalars. # selected_indices / top_k_intervals are 1-based. ``` ::: :::{tab-item} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- recursive_pls_fit(X, Y, n_components, window_size = 50L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} R · pls4all (formula+S3) :sync: r-formula :class-label: lang-r ```r library(pls4all) fit <- recursive_pls(y ~ ., data = train, ncomp = 3L) yhat <- predict(fit, newdata = test) summary(fit) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.recursive_pls(X, y, 3); % see header of bindings/matlab/+pls4all/recursive_pls.m for full % parameter surface: % res = recursive_pls(X, Y, n_components, window_size) yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab ```matlab mdl = pls4all.fit("recursive_pls", X, y, "NumComponents", 3); yhat = predict(mdl, Xtest); ``` ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`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 Adaptive wall-clock per cell measured against [`full_matrix.csv`](../benchmarks/overview.md). 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 = pls4all binding 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`](../benchmarks/methodology.md)). C++ and external rows show reference parity; pls4all language bindings show binding parity against the C++ backend. Hover the icon for role and tolerance band. ::::{tab-set} :class: parity-tabs :::{tab-item} 1 thread :sync: threads-1
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 9e-162.92 ms
Python · pls4all
pls4all.python✓ bind2.79 ms🏆
pls4all.sklearn✓ bind3.10 ms
R · pls4all
pls4all.R✓ 4e-155.74 ms
pls4all.R.formula✓ 4e-156.55 ms
pls4all.R.mdatools✓ 4e-156.99 ms
pls4all.R.pls✓ 4e-157.36 ms
Python · external
📐ref.python_scikit_learnsource48.1 ms
R · external
📐ref.r_pls⇄ +4e-15141.6 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 9e-162.87 ms🏆
Python · pls4all
pls4all.python✓ bind2.94 ms
pls4all.sklearn✓ bind3.11 ms
R · pls4all
pls4all.R✓ 4e-155.97 ms
pls4all.R.formula✓ 4e-156.97 ms
pls4all.R.mdatools✓ 4e-157.91 ms
pls4all.R.pls✓ 4e-156.92 ms
Python · external
📐ref.python_scikit_learnsource46.3 ms
R · external
📐ref.r_pls⇄ +4e-15144.8 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 9e-162.95 ms🏆
Python · pls4all
pls4all.python✓ bind3.02 ms
pls4all.sklearn✓ bind3.06 ms
R · pls4all
pls4all.R✓ 4e-155.98 ms
pls4all.R.formula✓ 4e-157.42 ms
pls4all.R.mdatools✓ 4e-156.94 ms
pls4all.R.pls✓ 4e-157.32 ms
Python · external
📐ref.python_scikit_learnsource48.7 ms
R · external
📐ref.r_pls⇄ +4e-15147.3 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)