alibi.utils.distance

Functions

abdm

abdm(X: numpy.ndarray, cat_vars: dict, cat_vars_bin: dict = {})

Calculate the pair-wise distances between categories of a categorical variable using the Association-Based Distance Metric based on Le et al (2005). http://www.jaist.ac.jp/~bao/papers/N26.pdf

Name	Type	Default	Description
X	numpy.ndarray		Batch of arrays.
cat_vars	dict		Dict with as keys the categorical columns and as optional values the number of categories per categorical variable.
cat_vars_bin	dict	{}	Dict with as keys the binned numerical columns and as optional values the number of bins per variable.

batch_compute_kernel_matrix

batch_compute_kernel_matrix(x: Union[list, numpy.ndarray], y: Union[list, numpy.ndarray], kernel: Callable[[.[<class 'numpy.ndarray'>, <class 'numpy.ndarray'>]], numpy.ndarray], batch_size: int = 10000000000, preprocess_fn: Optional[Callable[[.[typing.Union[list, numpy.ndarray]]], numpy.ndarray]] = None) -> numpy.ndarray

Compute the kernel matrix between x and y by filling in blocks of size batch_size x batch_size at a time.

Name	Type	Default	Description
x	Union[list, numpy.ndarray]		The first list/numpy array of data instances.
y	Union[list, numpy.ndarray]		The second list/numpy array of data instances.
kernel	Callable[[.[<class 'numpy.ndarray'>, <class 'numpy.ndarray'>]], numpy.ndarray]		Kernel function to be used for kernel matrix computation.
batch_size	int	10000000000	Batch size to be used for each prediction.
preprocess_fn	Optional[Callable[[.[typing.Union[list, numpy.ndarray]]], numpy.ndarray]]	None	Optional preprocessing function for each batch.

Returns

• Type: numpy.ndarray

cityblock_batch

cityblock_batch(X: numpy.ndarray, y: numpy.ndarray) -> numpy.ndarray

Calculate the L1 distances between a batch of arrays X and an array of the same shape y.

Name	Type	Default	Description
X	numpy.ndarray		Batch of arrays to calculate the distances from.
y	numpy.ndarray		Array to calculate the distance to.

Returns

• Type: numpy.ndarray

multidim_scaling

multidim_scaling(d_pair: dict, feature_range: Tuple[numpy.ndarray, numpy.ndarray], n_components: int = 2, use_metric: bool = True, standardize_cat_vars: bool = True, smooth: float = 1.0, center: bool = True, update_feature_range: bool = True) -> Tuple[dict, tuple]

Apply multidimensional scaling to pairwise distance matrices.

Name	Type	Default	Description
d_pair	dict		Dict with as keys the column index of the categorical variables and as values a pairwise distance matrix for the categories of the variable.
feature_range	Tuple[numpy.ndarray, numpy.ndarray]		Tuple with min and max ranges to allow for perturbed instances. Min and max ranges are numpy arrays with dimension (1 x nb of features).
n_components	int	2	Number of dimensions in which to immerse the dissimilarities.
use_metric	bool	True	If True, perform metric MDS; otherwise, perform nonmetric MDS.
standardize_cat_vars	bool	True	Standardize numerical values of categorical variables if True.
smooth	float	1.0	Smoothing exponent between 0 and 1 for the distances. Lower values than 1 will smooth the difference in distance metric between different features.
center	bool	True	Whether to center the scaled distance measures. If False, the min distance for each feature except for the feature with the highest raw max distance will be the lower bound of the feature range, but the upper bound will be below the max feature range.
update_feature_range	bool	True	Update feature range with scaled values.

Returns

• Type: Tuple[dict, tuple]

mvdm

mvdm(X: numpy.ndarray, y: numpy.ndarray, cat_vars: dict, alpha: int = 1) -> Dict[int, numpy.ndarray]

Calculate the pair-wise distances between categories of a categorical variable using the Modified Value Difference Measure based on Cost et al (1993). https://link.springer.com/article/10.1023/A:1022664626993

Name	Type	Default	Description
X	numpy.ndarray		Batch of arrays.
y	numpy.ndarray		Batch of labels or predictions.
cat_vars	dict		Dict with as keys the categorical columns and as optional values the number of categories per categorical variable.
alpha	int	1	Power of absolute difference between conditional probabilities.

Returns

• Type: Dict[int, numpy.ndarray]

squared_pairwise_distance

squared_pairwise_distance(x: numpy.ndarray, y: numpy.ndarray, a_min: float = 1e-07, a_max: float = 1e+30) -> numpy.ndarray

numpy pairwise squared Euclidean distance between samples x and y.

Name	Type	Default	Description
x	numpy.ndarray		A batch of instances of shape Nx x features.
y	numpy.ndarray		A batch of instances of shape Ny x features.
a_min	float	1e-07	Lower bound to clip distance values.
a_max	float	1e+30	Upper bound to clip distance values.

Returns

• Type: numpy.ndarray