Functions for computing the Nogueira Stability Index, which measures the consistency of feature selection across cross-validation folds.
Details
The Nogueira Stability Index is preferred over Jaccard/Kuncheva indices because it is invariant to the number of selected features. A high stability (close to 1) indicates that the same features are consistently selected across different training subsets, suggesting robust signal rather than overfitting to specific data splits.
Formula: $$S = 1 - \frac{V}{V_0}$$
Where: - V = (1/p) * sum(pi_j * (1 - pi_j)) [observed variance] - V_0 = (k_bar/p) * (1 - k_bar/p) [expected variance under random selection] - pi_j = selection frequency for feature j - k_bar = average number of selected features - p = total number of candidate features