Implementation:Scikit learn Scikit learn ShrunkCovariance

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Covariance Estimation
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for regularized covariance estimation using shrinkage methods provided by scikit-learn.

Description

This module implements several shrinkage-based covariance estimators. Shrinkage regularizes the empirical covariance by combining it with a structured target (scaled identity). The module provides ShrunkCovariance with a fixed shrinkage parameter, LedoitWolf with analytically optimal shrinkage, and OAS (Oracle Approximating Shrinkage) with an alternative shrinkage formula. It also includes standalone functions ledoit_wolf, ledoit_wolf_shrinkage, and oas for direct computation without the estimator interface.

Usage

Use shrunk covariance estimators when the number of features is large relative to the number of samples, as the empirical covariance can be poorly conditioned or singular. LedoitWolf is recommended for automatic shrinkage selection.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/covariance/_shrunk_covariance.py

Signature

class ShrunkCovariance(EmpiricalCovariance):
    """Covariance estimator with shrinkage."""

    def __init__(self, *, store_precision=True, assume_centered=False, shrinkage=0.1):
        ...

class LedoitWolf(EmpiricalCovariance):
    """LedoitWolf Estimator."""

    def __init__(self, *, store_precision=True, assume_centered=False, block_size=1000):
        ...

class OAS(EmpiricalCovariance):
    """Oracle Approximating Shrinkage Estimator."""

    def __init__(self, *, store_precision=True, assume_centered=False):
        ...

Import

from sklearn.covariance import ShrunkCovariance, LedoitWolf, OAS

I/O Contract

Inputs

Name	Type	Required	Description
X	array-like of shape (n_samples, n_features)	Yes	Training data for covariance estimation
store_precision	bool	No	Whether to store precision matrix (default: True)
assume_centered	bool	No	Whether data is centered (default: False)
shrinkage	float	No	Shrinkage coefficient for ShrunkCovariance (default: 0.1)
block_size	int	No	Block size for LedoitWolf block computation (default: 1000)

Outputs

Name	Type	Description
covariance_	ndarray of shape (n_features, n_features)	Estimated shrunk covariance matrix
location_	ndarray of shape (n_features,)	Estimated location (mean)
precision_	ndarray of shape (n_features, n_features)	Estimated precision matrix
shrinkage_	float	Computed optimal shrinkage coefficient (LedoitWolf, OAS)

Usage Examples

Basic Usage

import numpy as np
from sklearn.covariance import LedoitWolf

# Generate high-dimensional data
rng = np.random.RandomState(42)
X = rng.randn(50, 100)  # n_features > n_samples

# Fit Ledoit-Wolf shrinkage estimator
lw = LedoitWolf().fit(X)
print("Shrinkage coefficient:", lw.shrinkage_)
print("Covariance shape:", lw.covariance_.shape)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Covariance_Estimation