# `pls_cox` — PLS-Cox (survival regression)
_Group_: **Classification & GLM** · _Registry tolerance_: `1e-06`
## Description
PLS-Cox (§5) — Cox PH on PLS scores
From the `pls4all.sklearn.PLSCoxRegressor` docstring:
> PLS + Cox proportional-hazards regression on PLS scores.
> **Registry note** — Bastien 2008 deviance-residual PLS-Cox (NumPy port): scale X, deviance residuals from a null Cox PH, NIPALS PLS, Breslow Cox NR on the scores. pls4all's default wrapper calls the same routine, so the gate is bit-for-bit. The legacy single-pass C++ kernel (SIMPLS on log-time pseudo-response) is opt-in via ``legacy=True``. R `plsRcox::coxsplsDR` is the published counterpart; see ``_PlsCoxRReference`` for the archived adapter.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `n_classes` | `int` | `2` | registry benchmark cell value |
## Explanations
### Bibliographic source
Bastien, P., Bertrand, F., Meyer, N. & Maumy-Bertrand, M. (2015). *Deviance residuals-based sparse PLS and sparse kernel PLS regression for censored data*. Bioinformatics 31(3), 397–404.
### Mathematical principle
Cox proportional-hazards regression with PLS-based dimensionality reduction. The Cox model $\lambda(t \mid \mathbf{x}) = \lambda_0(t)\exp(\mathbf{x}^{\top}\boldsymbol{\beta})$ is degenerate in $p \gg n$ because the partial likelihood loses identifiability. PLS-Cox replaces the $p$-dimensional $\boldsymbol{\beta}$ with a $k$-dimensional latent representation by extracting PLS scores from the **deviance residuals** of a null Cox model.
Required inputs are survival times and event indicators (0 = censored, 1 = event observed). The output is a fitted Cox model on the latent scores; risk scores for new samples are computed by first projecting them into the latent space and then evaluating $\mathbf{t}^{\top}\boldsymbol{\beta}$.
This is the canonical method in high-dimensional biomarker survival studies (RNA-seq, MALDI-TOF) where a direct Cox model is infeasible.
### Implementation
`n4m_pls_cox_fit`. Reference: R `plsRcox 1.8.2`.
MATLAB header (`bindings/matlab/+pls4all/pls_cox.m`):
```text
pls4all.pls_cox PLS-Cox proportional hazards (Breslow baseline hazard).
survival_times: numeric vector of length size(X, 1).
event_indicators: 0/1 integer vector of length size(X, 1).
```
### 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_pls_cox_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 pls_cox_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = pls_cox_fit(ctx, cfg, X, y, n_components=4, sample_weights=sample_w, y_labels=y_labels)
# 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 PLSCoxRegressor
mdl = PLSCoxRegressor(n_components=2)
mdl.fit(X, y, sample_weight=sample_w)
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("pls_cox", X, y,
n_components = 4L, params = list(n_classes = 2L))
# 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.pls_cox(X, y, 4);
% see header of bindings/matlab/+pls4all/pls_cox.m for full
% parameter surface:
% res = pls_cox(X, n_components, survival_times, event_indicators)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("pls_cox", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.python_numpy`** (python · python) — `numpy` in-tree · strict (rmse_rel ≤ 1e-06) — In-tree NumPy port of Bastien 2008 PLS-Cox (deviance residuals + NIPALS PLS + Breslow Cox PH). pls4all's default wrapper calls the same function, so the parity gate is bit-for-bit (max_abs < 1e-6). R `plsRcox::coxsplsDR` is the published algorithmic counterpart but differs at the 1e-3 level due to Efron ties + scaling conventions; the legacy single-pass C++ kernel (SIMPLS on log-time pseudo-response) is opt-in via ``legacy=True``.
:::
### 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 🏆.
**Reference gate**: strict — numeric equivalence (`rmse_rel_tol ≤ 1e-06`).
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
| 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) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ≈ | 6.26 ms | 3.27 ms | 11.7 ms🏆 | 66.1 ms | 1.78 ms🏆 | 4.08 ms | 7.45 ms | 60.9 ms | 334.0 ms🏆 | 46.0 ms | 357.0 ms | 1.9 s🏆 | 191.8 ms | 1.5 s |
pls4all.cpp.blas+omp | ≈ | 4.49 ms | 3.20 ms | 12.5 ms | 63.4 ms | 1.97 ms | 5.12 ms | 7.64 ms | 61.4 ms | 337.9 ms | 43.5 ms | 348.9 ms🏆 | 1.9 s | 176.0 ms🏆 | 1.5 s |
pls4all.cpp.omp | ≈ | 4.28 ms🏆 | 1.69 ms🏆 | 13.3 ms | 65.4 ms | 1.86 ms | 3.51 ms | 7.09 ms | 60.1 ms🏆 | 339.8 ms | 42.0 ms🏆 | 357.2 ms | 1.9 s | 178.1 ms | 1.5 s🏆 |
pls4all.cpp.ref | ≈ | 4.83 ms | 2.60 ms | 12.8 ms | 61.9 ms🏆 | 1.83 ms | 3.84 ms | 6.84 ms🏆 | 63.9 ms | 334.3 ms | 43.8 ms | 362.6 ms | 1.9 s | 200.9 ms | 1.5 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 6.37 ms | — | — | — | 1.87 ms | 3.64 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +7e+02 | 3.01 ms | — | — | — | 1.92 ms | 4.53 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +7e+02 | 11.0 ms | — | — | — | 5.10 ms | 11.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +7e+02 | 22.8 ms | — | — | — | 5.37 ms | 11.8 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +7e+02 | 21.9 ms | — | — | — | 6.66 ms | 10.7 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +7e+02 | 24.9 ms | — | — | — | 5.04 ms | 11.9 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +7e+02 | 4.41 ms | — | — | — | 2.40 ms | 5.03 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +7e+02 | 5.19 ms | — | — | — | 2.63 ms | 5.42 ms | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_numpy | source | 4.72 ms | — | — | — | 2.85 ms | 3.28 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) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 1.75 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 1.83 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 1.82 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 2.55 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 2.84 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +2e+00 | — | — | — | — | 2.24 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +2e+00 | — | — | — | — | 5.22 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +2e+00 | — | — | — | — | 5.03 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +2e+00 | — | — | — | — | 4.74 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +2e+00 | — | — | — | — | 5.13 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +2e+00 | — | — | — | — | 2.14 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +2e+00 | — | — | — | — | 2.61 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_numpy | source | — | — | — | — | 2.34 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) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 2.81 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 2.61 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 1.65 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 1.71 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 2.57 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +2e+00 | — | — | — | — | 1.38 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +2e+00 | — | — | — | — | 3.19 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +2e+00 | — | — | — | — | 3.92 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +2e+00 | — | — | — | — | 3.86 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +2e+00 | — | — | — | — | 3.83 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +2e+00 | — | — | — | — | 1.97 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +2e+00 | — | — | — | — | 2.32 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_numpy | source | — | — | — | — | 1.66 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)