L-infinity histogram gap

humancompatible.detect.methods.l_inf.l_inf.check_l_inf_gap(X: ndarray, y: ndarray, binarizer: Binarizer, feature_involved: str, subgroup_to_check: Any, delta: float) → float

Test whether a protected subgroup’s outcome distribution differs from the overall population by at most delta in the l_inf-norm.

Parameters:

• X (np.ndarray) – Protected-attribute slice of the dataset (same rows as y).

• y (np.ndarray) – Boolean target vector.

• binarizer (Binarizer) – The binarizer used to encode X and y.

• feature_involved (str) – Name of the protected column whose subgroup is tested.

• subgroup_to_check (Any) – Raw value of the subgroup to isolate.

• delta (float) – Threshold for the L-infinity norm.

Returns:

1.0 (which means True) if the subgroup histogram is within delta;

0.0 (which means False) otherwise.

Return type:

float

Raises:

• ValueError – If delta is not positive.

• KeyError – If feature_involved is not in the binarizer’s feature names.

• KeyError – If subgroup_to_check is not a valid value for the feature.

humancompatible.detect.methods.l_inf.lp_tools.lin_prog_feas(hist1: ndarray, hist2: ndarray, delta: float, num_samples: float = 1.0) → int

Specifies a number of samples as a fraction of the total histogram bins and checks whether all the sampled bins satisfy

|hist1 - hist2| <= delta.

Parameters:

• hist1 (np.ndarray) – 1-D array of histogram bin densities for the full dataset.

• hist2 (np.ndarray) – 1-D array of histogram bin densities for the subgroup.

• delta (float) – Threshold for the absolute difference |hist1 - hist2|.

• num_samples (float) – Fraction of total bins to sample. The function draws int(num_samples * (len(hist1) - 1)) random samples.

Returns:

Status code from scipy.optimize.linprog. A status of 0 indicates

the constraints are feasible (i.e., |hist1 - hist2| <= delta for all sampled bins); other codes signal infeasibility or solver errors.

Return type:

int