LedoitWolf

#include <Skigen/Covariance>

template <typename Scalar = double>
class Skigen::LedoitWolf(assume_centered=false)

Ledoit-Wolf shrinkage covariance estimator.

Estimates the covariance matrix using the Ledoit-Wolf shrinkage method, which analytically computes the optimal shrinkage coefficient that minimizes the Frobenius norm of the estimation error.

The estimator computes:

$$\hat{\Sigma} = (1 - \alpha)\,S + \alpha\,\mu\,I$$

where $S$ is the sample covariance (normalized by $n$), $\mu = \mathrm{tr}(S)/p$ is the mean eigenvalue, and $\alpha \in [0,1]$ is the optimal shrinkage coefficient.

Reference: Ledoit & Wolf (2004), "A well-conditioned estimator for large-dimensional covariance matrices", Journal of Multivariate Analysis, 88(2), 365-411.

Mirrors sklearn.covariance.LedoitWolf.

---

Parameters:

• assume_centered : bool, default=false If true, data is assumed to be centered and mean is not subtracted (bool, default false).

---

Attributes:

• covariance : MatrixType Estimated covariance matrix (p × p).

• shrinkage : Scalar Optimal shrinkage coefficient α ∈ [0, 1].

• location : RowVectorType Estimated location (mean) of the data (1 × p).

---

Methods

fit(X)

Fit the Ledoit-Wolf covariance model.

Parameters:

• X : MatrixType Data matrix of shape (n_samples, n_features).

Returns:

• result : LedoitWolf Reference to the fitted estimator (*this).

---

score(X)

Return the Gaussian log-likelihood of X under the fitted model.

Parameters:

• X : MatrixType Data matrix of shape (n_samples, n_features).

Returns:

• result : Scalar Average log-likelihood per sample.

---

Example

Skigen::LedoitWolf<double> lw;
lw.fit(X);

std::cout << "=== LedoitWolf ===\n"
          << "Shrinkage coefficient: " << lw.shrinkage() << "\n"
          << "Covariance (4x4):\n" << lw.covariance() << "\n\n";

---