dataeval.core.mutual_info¶

dataeval.core.mutual_info(class_labels, factor_data, discrete_features=None, num_neighbors=5)¶

Mutual information between factors (class label, metadata, label/image properties), transformed to lie in [0, 1].

Parameters:¶

class_labels : Array1D[int]¶: Target class labels as integer indices. Can be a 1D list, or array-like object.
factor_data : Array2D[int | float]¶: Factor values after binning or digitization. Can be a 2D list, or array-like object.
discrete_features : Array1D[bool] | None = None¶: Boolean array defining whether or not the feature set is discretized. Can be a 1D list, or array-like object.
num_neighbors : int = 5¶: Number of points to consider as neighbors.

Returns:¶

TypedDict containing:

class_to_factor: NDArray[np.float64] - 1D array of MI between class labels and each factor
interfactor: NDArray[np.float64] - (num_factors) x (num_factors) matrix of MI between factors only

Return type:¶

MutualInfoResult

Notes

We use mutual_info_classif from sklearn since class label is categorical. mutual_info_classif outputs are consistent up to O(1e-4) and depend on a random seed. MI is computed differently for categorical and continuous variables. With continuous variables, since there is no upper limit to the entropy of a continuous distribution, normalization by entropy becomes problematic. So instead we transform mutual information into a balance metric using the Linfoot transformation.

References

[1] Linfoot, E.H. (1957). “An Informational Measure of Correlation.” Information and Control, 1(1), 85-89.

Example

Return balance (mutual information) of factors with class_labels

>>> class_labels, binned_data = generate_random_class_labels_and_binned_data(
...     labels=["doctor", "artist", "teacher"],
...     factors={"age": [25, 30, 35, 45], "income": [50000, 65000, 80000], "gender": ["M", "F"]},
...     length=100,
...     random_seed=175,
... )

>>> result = mutual_info(class_labels=class_labels, factor_data=binned_data)
>>> result["class_to_factor"]
array([0.888, 0.251, 0.004, 0.363])
>>> result["interfactor"]
array([[1.   , 0.046, 0.078],
       [0.046, 1.   , 0.048],
       [0.078, 0.048, 1.   ]])