scikit-opls

Orthogonal Projections to Latent Structures (OPLS / OPLS-DA) with a scikit-learn interface.

OPLS (Trygg & Wold, 2002) splits the variation in X into a predictive part correlated with the response and orthogonal parts that are not. scikit-opls removes the orthogonal variation with an OSC-style orthogonal filter and then fits sklearn.cross_decomposition.PLSRegression on the cleaned X as the predictive engine. With n_orthogonal=0 the model reduces exactly to PLSRegression.

Install

Requires Python 3.12+.

pip install scikit-opls

Plotting is an opt-in extra, since matplotlib is only imported by scikit_opls.plotting:

pip install "scikit-opls[plot]"

With uv: uv add scikit-opls. To work on the package itself, see Development.

Usage

OPLS regression

import numpy as np
from scikit_opls import OPLS

rng = np.random.default_rng(0)
X = rng.normal(size=(100, 50))
y = X[:, 0] * 2.0 + rng.normal(scale=0.1, size=100)

model = OPLS(n_components=1, n_orthogonal=2, scale="standard").fit(X, y)

model.predict(X)  # predictions
model.transform(X)  # predictive scores
model.transform_orthogonal(X)  # orthogonal scores
model.filter_transform(X)  # preprocessed, orthogonal-filtered X fed to the engine
model.r2x_, model.r2y_  # fit summaries
model.vip_  # variable importance (predictive), lazy property

The whole fitted pipeline (scaling → orthogonal filter → predictive PLS) is linear, so it collapses to coefficients on the raw input space:

y_hat = (X @ model.coef_raw_.T + model.intercept_raw_).ravel()  # == model.predict(X)

Let cross-validated Q2 choose the number of orthogonal components with scikit-learn's GridSearchCV — no bespoke estimator needed (scoring=None gives out-of-fold R2, which equals Q2 for OPLS):

from sklearn.model_selection import GridSearchCV
from scikit_opls import OPLS

search = GridSearchCV(
    OPLS(n_components=1), {"n_orthogonal": list(range(10))}, cv=7
).fit(X, y)
search.best_params_["n_orthogonal"]  # chosen count
search.best_estimator_  # final OPLS refit on all data
search.cv_results_["mean_test_score"]  # out-of-fold R2/Q2 path

For OPLS-DA, wrap OPLSDA() the same way; an int cv becomes stratified automatically and scoring="roc_auc" is usually preferable.

To bias toward fewer orthogonal components — prefer the smallest count whose mean score is within a tolerance of the best — pass a refit callable:

import numpy as np


def parsimonious_refit(cv_results, tol=0.01):
    scores = np.asarray(cv_results["mean_test_score"], dtype=float)
    counts = np.asarray(cv_results["param_n_orthogonal"], dtype=int)
    within = np.flatnonzero(scores >= np.nanmax(scores) - tol)
    return int(within[np.argmin(counts[within])])


GridSearchCV(
    OPLS(n_components=1),
    {"n_orthogonal": list(range(10))},
    cv=7,
    refit=parsimonious_refit,
).fit(X, y)

OPLS-DA (binary classification)

from scikit_opls import OPLSDA

y = np.where(X[:, 0] > 0, "case", "ctrl")
clf = OPLSDA(n_components=1, n_orthogonal=2).fit(X, y)

clf.predict(X)  # class labels
clf.decision_function(X)  # raw signed OPLS regression output
clf.opls_.transform(X)  # predictive scores of the underlying OPLS model

# Probabilities: wrap in a cross-fitted calibrator when each class has enough
# samples for the chosen calibration CV split.
from sklearn.calibration import CalibratedClassifierCV

CalibratedClassifierCV(clf, cv=5).fit(X, y).predict_proba(X)

O2PLS (two-block)

O2PLS models two blocks jointly, separating the covariation they share from the structured variation specific to each, and predicts in both directions.

from scikit_opls import O2PLS

T = rng.normal(size=(100, 2))
Xb = T @ rng.normal(size=(2, 20)) + 0.1 * rng.normal(size=(100, 20))
Yb = T @ rng.normal(size=(2, 5)) + 0.1 * rng.normal(size=(100, 5))

o2 = O2PLS(n_components=2, n_x_orthogonal=1, n_y_orthogonal=1).fit(Xb, Yb)

o2.predict(Xb)  # Y from X
o2.predict_x(Yb)  # X from Y
o2.transform(Xb)  # joint X scores
o2.transform_orthogonal_x(Xb)  # X-specific orthogonal scores
o2.r2x_, o2.r2y_  # joint fit summaries

Diagnostics

Plotting needs the optional plot extra (pip install "scikit-opls[plot]"); it follows scikit-learn's Display convention.

from scikit_opls.plotting import OPLSScoresDisplay, SPlotDisplay
from scikit_opls.validation import permutation_test

# Draw score plot (t_pred vs t_ortho). Supports component selection for multi-component PLS
OPLSScoresDisplay.from_estimator(
    model, X, y, predictive_component=0, orthogonal_component=0
)

# Draw S-plot (covariance vs correlation) for a specific predictive component
SPlotDisplay.from_estimator(model, X, component=0)

# Permutation significance testing
permutation_test(OPLS(n_orthogonal=2), X, y)

Note

Pipeline support in plotting: Diagnostic plotting displays support OPLS, OPLSDA, and pipelines ending in one. For tuned models, pass search.best_estimator_ explicitly. When passing a pipeline, pass raw X as expected by the pipeline. When passing the final OPLS step directly, pass the already transformed matrix. For pipeline S-plots, points are in the transformed feature space received by the final OPLS step.

Example datasets

Two runnable scripts live under examples/, and CI executes both on every push:

uv run python examples/palmerpenguins_opls_regression.py  # OPLS regression
uv run python examples/o2pls_synthetic.py                 # two-block O2PLS

The penguins example reads its CSV straight from a GitHub release asset with pandas.read_csv, so no dataset is stored in the checkout:

• https://github.com/HauserGroup/scikit-opls/releases/download/data/palmerpenguins.csv

Parameters

Parameter	Meaning
n_components	Predictive components (classic OPLS uses 1).
n_orthogonal	Orthogonal components to remove (int; tune via GridSearchCV).
scale	"none", "center", "pareto", "standard".

OPLSDA takes the same parameters. O2PLS replaces n_orthogonal with n_x_orthogonal and n_y_orthogonal, one per block.

Wrap OPLS in GridSearchCV over n_orthogonal for cross-validated selection (see the snippet above); cv, scoring and n_jobs come from GridSearchCV.

Development

uv sync --dev              # install the project and dev tools
uv run pre-commit install  # enable the git hooks (run once)

uv run pytest --cov        # tests + coverage (incl. sklearn check_estimator)
uv run ruff check          # lint
uv run ruff format --check # format check
uv run pyright src         # type-check
uv run pre-commit run --all-files  # run every hook

See CONTRIBUTING.md for the full contributor workflow.

References

This project is inspired by the R ropls package and uses the orthogonal-scores PLS algorithm of pls::oscorespls.fit as its engine.

• Trygg, J. & Wold, S. (2002). Orthogonal projections to latent structures (O-PLS). Journal of Chemometrics, 16(3), 119–128. doi:10.1002/cem.695
• Trygg, J. & Wold, S. (2003). O2-PLS, a two-block (X–Y) latent variable regression (LVR) method with an integral OSC filter. Journal of Chemometrics, 17(1), 53–64. doi:10.1002/cem.775
• Wold, S., Antti, H., Lindgren, F. & Öhman, J. (1998). Orthogonal signal correction of near-infrared spectra. Chemometrics and Intelligent Laboratory Systems, 44(1–2), 175–185. doi:10.1016/S0169-7439(98)00109-9
• Bylesjö, M., Rantalainen, M., Cloarec, O., Nicholson, J. K., Holmes, E. & Trygg, J. (2006). OPLS discriminant analysis: combining the strengths of PLS-DA and SIMCA classification. Journal of Chemometrics, 20(8–10), 341–351. doi:10.1002/cem.1006
• Galindo-Prieto, B., Eriksson, L. & Trygg, J. (2014). Variable influence on projection (VIP) for OPLS models. Journal of Chemometrics, 28(8), 623–632. doi:10.1002/cem.2627

Citing

If scikit-opls supports published work, please cite the software and the methods above. Citation metadata lives in CITATION.cff; GitHub renders a formatted citation from it under Cite this repository. See the Citing page for BibTeX.

License

MIT.