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# Copyright 2021 The HuggingFace Datasets Authors and the current dataset script contributor.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Mahalanobis metric."""
import datasets
import numpy as np
import evaluate
_DESCRIPTION = """
Compute the Mahalanobis Distance
Mahalonobis distance is the distance between a point and a distribution.
And not between two distinct points. It is effectively a multivariate equivalent of the Euclidean distance.
It was introduced by Prof. P. C. Mahalanobis in 1936
and has been used in various statistical applications ever since
[source: https://www.machinelearningplus.com/statistics/mahalanobis-distance/]
"""
_CITATION = """\
@article{de2000mahalanobis,
title={The mahalanobis distance},
author={De Maesschalck, Roy and Jouan-Rimbaud, Delphine and Massart, D{\'e}sir{\'e} L},
journal={Chemometrics and intelligent laboratory systems},
volume={50},
number={1},
pages={1--18},
year={2000},
publisher={Elsevier}
}
"""
_KWARGS_DESCRIPTION = """
Args:
X: List of datapoints to be compared with the `reference_distribution`.
reference_distribution: List of datapoints from the reference distribution we want to compare to.
Returns:
mahalanobis: The Mahalonobis distance for each datapoint in `X`.
Examples:
>>> mahalanobis_metric = evaluate.load("mahalanobis")
>>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])
>>> print(results)
{'mahalanobis': array([0.5])}
"""
@evaluate.utils.file_utils.add_start_docstrings(_DESCRIPTION, _KWARGS_DESCRIPTION)
class Mahalanobis(evaluate.Metric):
def _info(self):
return evaluate.MetricInfo(
description=_DESCRIPTION,
citation=_CITATION,
inputs_description=_KWARGS_DESCRIPTION,
features=datasets.Features(
{
"X": datasets.Sequence(datasets.Value("float", id="sequence"), id="X"),
}
),
)
def _compute(self, X, reference_distribution):
# convert to numpy arrays
X = np.array(X)
reference_distribution = np.array(reference_distribution)
# Assert that arrays are 2D
if len(X.shape) != 2:
raise ValueError("Expected `X` to be a 2D vector")
if len(reference_distribution.shape) != 2:
raise ValueError("Expected `reference_distribution` to be a 2D vector")
if reference_distribution.shape[0] < 2:
raise ValueError(
"Expected `reference_distribution` to be a 2D vector with more than one element in the first dimension"
)
# Get mahalanobis distance for each prediction
X_minus_mu = X - np.mean(reference_distribution)
cov = np.cov(reference_distribution.T)
try:
inv_covmat = np.linalg.inv(cov)
except np.linalg.LinAlgError:
inv_covmat = np.linalg.pinv(cov)
left_term = np.dot(X_minus_mu, inv_covmat)
mahal_dist = np.dot(left_term, X_minus_mu.T).diagonal()
return {"mahalanobis": mahal_dist}
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