holisticai.bias.metrics.gini_index

holisticai.bias.metrics.gini_index(mat_pred, top=None, thresh=0.5, normalize=False)

GINI index

Measures the inequality across the frequency distribution of the recommended items.

Interpretation

An algorithm that recommends each item the same number of times (uniform distribution) will have a Gini index of 0 and the one with extreme inequality will have a Gini of 1.

Parameters

mat_predmatrix-like

Matrix with shape (num_users, num_items). A recommender score (binary or soft pred) for each user,item interaction.

topint, optional

If not None, the number of items that are shown to each user.

threshfloat, optional

Threshold indicating value at which a given item is shown to user (if top is None).

normalizebool, optional

If True, normalises the data matrix to [0,1] range.

Returns

float

GINI

References

[1]

M Mansoury, H Abdollahpouri, M Pechenizkiy, B Mobasher, R Burke (2020). FairMatch: A Graph-based Approach for Improving Aggregate Diversity in Recommender Systems, <https://doi.org/10.48550/arXiv.2005.01148>

[2]

Farzad Eskandanian, Bamshad Mobasher (2020). Using Stable Matching to Optimize the Balance between Accuracy and Diversity in Recommendation <https://doi.org/10.48550/arXiv.2006.03715>

Examples

>>> import numpy as np
>>> from holisticai.bias.metrics import gini_index
>>> mat_pred = np.array([[0.9, 0.8, 0.4, 0.2],
                      [0.7, 0.9, 0.1, 0.7],
                      [0.3, 0.2, 0.3, 0.3],
                      [0.2, 0.1, 0.7, 0.8],
                      [0.8, 0.7, 0.9, 0.1],
                      [1. , 0.9, 0.3, 0.6],
                      [0.8, 0.9, 0.1, 0.1],
                      [0.2, 0.3, 0.1, 0.5],
                      [0.1, 0.2, 0.7, 0.7],
                      [0.2, 0.7, 0.1, 0.2]])
>>> gini_index(mat_pred, top=2, thresh=None, normalize=False)
0.1333333333333333