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# Copyright The Lightning team.
#
# 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.
import itertools
from typing import Optional
import torch
from torch import Tensor
from typing_extensions import Literal
from torchmetrics.functional.classification.confusion_matrix import _multiclass_confusion_matrix_update
from torchmetrics.functional.nominal.utils import (
_compute_bias_corrected_values,
_compute_chi_squared,
_drop_empty_rows_and_cols,
_handle_nan_in_data,
_nominal_input_validation,
_unable_to_use_bias_correction_warning,
)
def _cramers_v_update(
preds: Tensor,
target: Tensor,
num_classes: int,
nan_strategy: Literal["replace", "drop"] = "replace",
nan_replace_value: Optional[float] = 0.0,
) -> Tensor:
"""Compute the bins to update the confusion matrix with for Cramer's V calculation.
Args:
preds: 1D or 2D tensor of categorical (nominal) data
target: 1D or 2D tensor of categorical (nominal) data
num_classes: Integer specifying the number of classes
nan_strategy: Indication of whether to replace or drop ``NaN`` values
nan_replace_value: Value to replace ``NaN`s when ``nan_strategy = 'replace```
Returns:
Non-reduced confusion matrix
"""
preds = preds.argmax(1) if preds.ndim == 2 else preds
target = target.argmax(1) if target.ndim == 2 else target
preds, target = _handle_nan_in_data(preds, target, nan_strategy, nan_replace_value)
return _multiclass_confusion_matrix_update(preds, target, num_classes)
def _cramers_v_compute(confmat: Tensor, bias_correction: bool) -> Tensor:
"""Compute Cramers' V statistic based on a pre-computed confusion matrix.
Args:
confmat: Confusion matrix for observed data
bias_correction: Indication of whether to use bias correction.
Returns:
Cramer's V statistic
"""
confmat = _drop_empty_rows_and_cols(confmat)
cm_sum = confmat.sum()
chi_squared = _compute_chi_squared(confmat, bias_correction)
phi_squared = chi_squared / cm_sum
num_rows, num_cols = confmat.shape
if bias_correction:
phi_squared_corrected, rows_corrected, cols_corrected = _compute_bias_corrected_values(
phi_squared, num_rows, num_cols, cm_sum
)
if torch.min(rows_corrected, cols_corrected) == 1:
_unable_to_use_bias_correction_warning(metric_name="Cramer's V")
return torch.tensor(float("nan"), device=confmat.device)
cramers_v_value = torch.sqrt(phi_squared_corrected / torch.min(rows_corrected - 1, cols_corrected - 1))
else:
cramers_v_value = torch.sqrt(phi_squared / min(num_rows - 1, num_cols - 1))
return cramers_v_value.clamp(0.0, 1.0)
def cramers_v(
preds: Tensor,
target: Tensor,
bias_correction: bool = True,
nan_strategy: Literal["replace", "drop"] = "replace",
nan_replace_value: Optional[float] = 0.0,
) -> Tensor:
r"""Compute `Cramer's V`_ statistic measuring the association between two categorical (nominal) data series.
.. math::
V = \sqrt{\frac{\chi^2 / n}{\min(r - 1, k - 1)}}
where
.. math::
\chi^2 = \sum_{i,j} \ frac{\left(n_{ij} - \frac{n_{i.} n_{.j}}{n}\right)^2}{\frac{n_{i.} n_{.j}}{n}}
where :math:`n_{ij}` denotes the number of times the values :math:`(A_i, B_j)` are observed with :math:`A_i, B_j`
represent frequencies of values in ``preds`` and ``target``, respectively.
Cramer's V is a symmetric coefficient, i.e. :math:`V(preds, target) = V(target, preds)`.
The output values lies in [0, 1] with 1 meaning the perfect association.
Args:
preds: 1D or 2D tensor of categorical (nominal) data
- 1D shape: (batch_size,)
- 2D shape: (batch_size, num_classes)
target: 1D or 2D tensor of categorical (nominal) data
- 1D shape: (batch_size,)
- 2D shape: (batch_size, num_classes)
bias_correction: Indication of whether to use bias correction.
nan_strategy: Indication of whether to replace or drop ``NaN`` values
nan_replace_value: Value to replace ``NaN``s when ``nan_strategy = 'replace'``
Returns:
Cramer's V statistic
Example:
>>> from torch import randint, round
>>> from torchmetrics.functional.nominal import cramers_v
>>> preds = randint(0, 4, (100,))
>>> target = round(preds + torch.randn(100)).clamp(0, 4)
>>> cramers_v(preds, target)
tensor(0.5284)
"""
_nominal_input_validation(nan_strategy, nan_replace_value)
num_classes = len(torch.cat([preds, target]).unique())
confmat = _cramers_v_update(preds, target, num_classes, nan_strategy, nan_replace_value)
return _cramers_v_compute(confmat, bias_correction)
def cramers_v_matrix(
matrix: Tensor,
bias_correction: bool = True,
nan_strategy: Literal["replace", "drop"] = "replace",
nan_replace_value: Optional[float] = 0.0,
) -> Tensor:
r"""Compute `Cramer's V`_ statistic between a set of multiple variables.
This can serve as a convenient tool to compute Cramer's V statistic for analyses of correlation between categorical
variables in your dataset.
Args:
matrix: A tensor of categorical (nominal) data, where:
- rows represent a number of data points
- columns represent a number of categorical (nominal) features
bias_correction: Indication of whether to use bias correction.
nan_strategy: Indication of whether to replace or drop ``NaN`` values
nan_replace_value: Value to replace ``NaN``s when ``nan_strategy = 'replace'``
Returns:
Cramer's V statistic for a dataset of categorical variables
Example:
>>> from torch import randint
>>> from torchmetrics.functional.nominal import cramers_v_matrix
>>> matrix = randint(0, 4, (200, 5))
>>> cramers_v_matrix(matrix)
tensor([[1.0000, 0.0637, 0.0000, 0.0542, 0.1337],
[0.0637, 1.0000, 0.0000, 0.0000, 0.0000],
[0.0000, 0.0000, 1.0000, 0.0000, 0.0649],
[0.0542, 0.0000, 0.0000, 1.0000, 0.1100],
[0.1337, 0.0000, 0.0649, 0.1100, 1.0000]])
"""
_nominal_input_validation(nan_strategy, nan_replace_value)
num_variables = matrix.shape[1]
cramers_v_matrix_value = torch.ones(num_variables, num_variables, device=matrix.device)
for i, j in itertools.combinations(range(num_variables), 2):
x, y = matrix[:, i], matrix[:, j]
num_classes = len(torch.cat([x, y]).unique())
confmat = _cramers_v_update(x, y, num_classes, nan_strategy, nan_replace_value)
cramers_v_matrix_value[i, j] = cramers_v_matrix_value[j, i] = _cramers_v_compute(confmat, bias_correction)
return cramers_v_matrix_value
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