# `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_mir_pls_fit`. No widely installable library reference; treated as `paper_only` in the registry.
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_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} 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 · ✗ divergent · ⚠ error · — not run. The fastest backend per column is marked 🏆.
::::{tab-set}
:class: parity-tabs
:::{tab-item} 1 thread
:sync: threads-1
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×30 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 2.78 ms🏆 | — | — | — | 1.35 ms🏆 | 2.67 ms🏆 | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 5e-15 | 3.02 ms | — | — | — | 1.76 ms | 3.00 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | 16.2 ms | — | — | — | 5.07 ms | 12.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | 21.8 ms | — | — | — | 4.89 ms | 10.6 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | 21.8 ms | — | — | — | 5.52 ms | 10.0 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | 23.0 ms | — | — | — | 6.74 ms | 9.21 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+01 | 4.33 ms | — | — | — | 2.01 ms | 4.12 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+01 | 5.50 ms | — | — | — | 2.57 ms | 5.43 ms | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×30 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 1.21 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 3e-15 | — | — | — | — | 1.62 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 3.71 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 5.30 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 4.79 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 4.63 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+01 | — | — | — | — | 1.93 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+01 | — | — | — | — | 2.38 ms | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×30 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 1.99 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 3e-15 | — | — | — | — | 1.31 ms🏆 | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 3.17 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 3.92 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 3.74 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 3.70 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+01 | — | — | — | — | 1.86 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+01 | — | — | — | — | 2.22 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)