gpr_pls — Gaussian Process on PLS scores

Group: Nonlinear / local · Registry tolerance: 1e-08

Description

GPR-on-PLS — RBF Gaussian Process on PLS scores (§47)

From the pls4all.sklearn.GPRPLSRegression docstring:

Gaussian-process head on SIMPLS training scores.

Registry note — GP head parity (sklearn GaussianProcessRegressor with RBF+WhiteKernel, optimizer=None) on the same PLS scores. Architecturally separated to allow GPR-on-AOMPLS reuse of fit_gp_on_scores.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

length_scale

float

1.0

noise_level

float

0.001

seed

int

0

Random seed for reproducible sampling/initialization.

Explanations

Bibliographic source

Bishop, C. M. (2006). Pattern Recognition and Machine Learning, §6.4 (Gaussian Processes). — combined with a preliminary PLS dimensionality reduction for spectroscopy.

Mathematical principle

Spectroscopic data are too high-dimensional for a direct Gaussian Process: GP inference is \(O(n^3)\) in samples but the kernel quality degrades rapidly when \(p\) exceeds a few hundred — most pairwise distances become near-identical, the kernel matrix loses contrast and the GP under-fits.

GPR-PLS solves this by first projecting \(\mathbf{X} \to \mathbf{T} = \mathbf{X}\mathbf{W}\) into a low-dimensional PLS latent space and then training a GP on \(\mathbf{T}\). The latent space preserves the variance most relevant to \(y\), the GP captures smooth non-linear residual structure, and the kernel matrix is well-conditioned because pairwise distances in \(\mathbb{R}^k\) remain informative.

Default kernel: RBF with length scale \(\ell\) and amplitude \(\sigma_f^2\), plus an isotropic noise variance \(\sigma_n^2\). Marginal-likelihood maximisation selects the three hyperparameters; pls4all uses a fixed-iteration L-BFGS pass to keep the cost bounded per cell.

Implementation

n4m_gpr_pls_fit. Reference: sklearn GaussianProcessRegressor with an RBF kernel applied to the score matrix from a separate sklearn PLSRegression.

MATLAB header (bindings/matlab/+pls4all/gpr_pls.m):

pls4all.gpr_pls  GPR on PLS scores (RBF kernel, single-target Y).

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

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_gpr_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);

import pls4all
from pls4all._methods import gpr_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = gpr_pls_fit(ctx, cfg, X, y, n_components=3)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import GPRPLSRegression
mdl = GPRPLSRegression(n_components=2, length_scale=1.0, noise_level=0.001, seed=0)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("gpr_pls", X, y,
                      n_components = 3L, params = list(length_scale = 1.0, noise_level = 0.001, seed = 0L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.gpr_pls(X, y, 3);
% see header of bindings/matlab/+pls4all/gpr_pls.m for full
% parameter surface:
%   res = gpr_pls(X, Y, n_components, length_scale, noise_level, seed)
yhat = predict(res, Xtest);

No idiomatic classdef wrapper — invoke pls4all.fit("gpr_pls", X, y, …) directly from the unified MEX factory.

Registry parity references 📐

  • 📐 ref.python_scikit_learn (python · python) — scikit-learn 1.4.2 · strict (rmse_rel ≤ 1e-08) — sklearn GP head on the same PLS training scores pls4all produces. PLS rotation conventions diverge per-component; comparing the GP head on shared T isolates the novel stage.

Benchmarks

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 = 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). 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.

BackendParity120×25 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 2e-105.91 ms
Python · pls4all
pls4all.python✓ bind6.17 ms
pls4all.sklearn✓ bind2.75 ms
R · pls4all
pls4all.R✓ 2e-1320.9 ms
pls4all.R.formula✓ 2e-1312.6 ms
pls4all.R.mdatools✓ 2e-138.10 ms
pls4all.R.pls✓ 2e-1314.2 ms
Python · external
📐ref.python_scikit_learnsource2.25 ms🏆
BackendParity120×25 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 2e-101.14 ms🏆
Python · pls4all
pls4all.python✓ bind2.43 ms
pls4all.sklearn✓ bind2.72 ms
R · pls4all
pls4all.R✓ 2e-134.45 ms
pls4all.R.formula✓ 2e-135.61 ms
pls4all.R.mdatools✓ 2e-136.10 ms
pls4all.R.pls✓ 2e-136.64 ms
Python · external
📐ref.python_scikit_learnsource2.75 ms
BackendParity120×25 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 2e-101.14 ms🏆
Python · pls4all
pls4all.python✓ bind1.80 ms
pls4all.sklearn✓ bind1.39 ms
R · pls4all
pls4all.R✓ 2e-132.53 ms
pls4all.R.formula✓ 2e-133.11 ms
pls4all.R.mdatools✓ 2e-133.24 ms
pls4all.R.pls✓ 2e-133.10 ms
Python · external
📐ref.python_scikit_learnsource2.29 ms

See also: benchmark overview · methods index · interactive dashboard