# `mir_pls` — MIR-PLS (Mid-InfraRed PLS, regularised) _Group_: **Multi-block / cross-modal** · _Registry tolerance_: `0.05` · _Parity reference_: **paper-only** (Sjöblom, J., Svensson, O., Josefson, M., Kullberg, H. & Wold, S. (1998). An evaluation of orthogonal signal correction applied to calibration transfer of near infrared spectra. Chemom. Intell. Lab. Syst. 44(1-2), 229-244. (Inverse-regression PLS variant; no widely installable port.)) ## Description MIR-PLS — Inverse-regression PLS (§13) From the `pls4all.sklearn.MIRPLSRegression` docstring: > Multivariate Inverse Regression PLS (Sjöblom 1998). ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `n_components` | `int` | `2` | Number of latent components extracted (k). | ## Explanations ### Bibliographic source Sjöblom, J., Svensson, O., Josefson, M., Kullberg, H. & Wold, S. (1998). *An evaluation of orthogonal signal correction applied to calibration transfer of near infrared spectra*. Chemometrics and Intelligent Laboratory Systems 44(1–2), 229–244. — adapted for MIR regularisation conventions. ### Mathematical principle MIR-PLS is a PLS variant tuned to mid-infrared spectroscopy conventions: it operates in absorbance space, uses a different ridge constant on the inner regression, and exposes a coefficient-export path that matches the mid-IR community's expectations (sign and ordering of loadings agree with `plsregress` rather than `pls::plsr`). Algorithmically it is a SIMPLS variant with a fixed ridge constant in the inner regression and an alternate intercept derivation. The differences from plain PLS are numerical, not algorithmic — the resulting predictions are within FP noise of plain PLS for well-conditioned inputs but more stable on the highly-correlated columns typical of MIR FTIR spectra. ### Implementation `n4m_estimators_mir_pls_fit`. No widely installable library reference; treated as `paper_only` in the registry. R roxygen note (`sklearn_methods.R::mir_pls`): > MIR-PLS — formula entry point. MATLAB header (`bindings/matlab/+pls4all/MirRegression.m`): ```text pls4all.MirRegression — Multivariate Inverse Regression PLS. ``` ### 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_mir_pls_fit(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 mir_pls_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = mir_pls_fit(ctx, cfg, X, y, n_components=4) # 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 MIRPLSRegression mdl = MIRPLSRegression(n_components=2) 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("mir_pls", X, y, n_components = 4L) # 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 <- mir_pls_fit(X, Y, n_components) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} R · pls4all (formula+S3) :sync: r-formula :class-label: lang-r ```r library(pls4all) fit <- mir_pls(y ~ ., data = train, ncomp = 4L) yhat <- predict(fit, newdata = test) summary(fit) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.mir_pls(X, y, 4); % see header of bindings/matlab/+pls4all/mir_pls.m for full % parameter surface: % res = mir_pls(X, Y, n_components) yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab ```matlab mdl = pls4all.fit("mir_pls", X, y, "NumComponents", 4); yhat = predict(mdl, Xtest); ``` ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📜 **Paper-only** — no executable parity reference; the `pls4all` implementation is verified by a smoke fit only. Canonical citation: Sjöblom, J., Svensson, O., Josefson, M., Kullberg, H. & Wold, S. (1998). An evaluation of orthogonal signal correction applied to calibration transfer of near infrared spectra. Chemom. Intell. Lab. Syst. 44(1-2), 229-244. (Inverse-regression PLS variant; no widely installable port.) ::: ### 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 🏆. ::::{tab-set} :class: parity-tabs :::{tab-item} 1 thread :sync: threads-1
BackendParity200×30 (ms)
Python · pls4all
pls4all.python✓ bind1.27 ms🏆
pls4all.sklearn✓ 3e-151.47 ms
R · pls4all
pls4all.R✓ bind3.98 ms
pls4all.R.formula✓ bind4.72 ms
pls4all.R.mdatools✓ bind5.11 ms
pls4all.R.pls✓ bind5.04 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×30 (ms)
Python · pls4all
pls4all.python✓ bind1.29 ms🏆
pls4all.sklearn✓ 3e-151.43 ms
R · pls4all
pls4all.R✓ bind4.49 ms
pls4all.R.formula✓ bind5.07 ms
pls4all.R.mdatools✓ bind5.39 ms
pls4all.R.pls✓ bind4.94 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×30 (ms)
Python · pls4all
pls4all.python✓ bind1.99 ms
pls4all.sklearn✓ 3e-151.41 ms🏆
R · pls4all
pls4all.R✓ bind4.09 ms
pls4all.R.formula✓ bind5.05 ms
pls4all.R.mdatools✓ bind4.73 ms
pls4all.R.pls✓ bind4.83 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)