gemclus.gemini.MI

class gemclus.gemini.MI(epsilon=1e-12)

Implements the classical mutual information between cluster conditional probabilities and the complete data probabilities:

\[\mathcal{I} = \mathbb{E}_{y \sim p(y)}[\text{KL}(p(x|y)\|p(x))]\]

This class is a simplified shortcut for KLGEMINI(ovo=False).

Parameters:

epsilon: float, default=1e-12

The precision for clipping the prediction values in order to avoid numerical instabilities.

__init__(epsilon=1e-12)

compute_affinity(X, y=None)

Unused for f-divergences.

Returns:

None

evaluate(y_pred, affinity, return_grad=False)

Compute the GEMINI objective given the predictions \(p(y|x)\) and an affinity matrix. The computation must return as well the gradients of the GEMINI w.r.t. the predictions. Depending on the context, the affinity matrix affinity can be either a kernel matrix or a distance matrix resulting from the compute_affinity method.

Parameters:

y_pred: ndarray of shape (n_samples, n_clusters)

The conditional distribution (prediction) of clustering assignment per sample.

affinity: ndarray of shape (n_samples, n_samples)

The affinity matrix resulting from the compute_affinity method. The matrix must be symmetric.

return_grad: bool, default=False

If True, the method should return the gradient of the GEMINI w.r.t. the predictions \(p(y|x)\).

Returns:

gemini: float

The gemini score of the model given the predictions and affinities.

gradients: ndarray of shape (n_samples, n_clusters)

The derivative w.r.t. the predictions y_pred: \(\nabla_{p (y|x)} \mathcal{I}\)