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theils_u.py
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theils_u.py
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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.
from typing import Any, Optional, Sequence, Union
import torch
from torch import Tensor
from typing_extensions import Literal
from torchmetrics.functional.nominal.theils_u import _theils_u_compute, _theils_u_update
from torchmetrics.functional.nominal.utils import _nominal_input_validation
from torchmetrics.metric import Metric
from torchmetrics.utilities.imports import _MATPLOTLIB_AVAILABLE
from torchmetrics.utilities.plot import _AX_TYPE, _PLOT_OUT_TYPE
if not _MATPLOTLIB_AVAILABLE:
__doctest_skip__ = ["TheilsU.plot"]
class TheilsU(Metric):
r"""Compute `Theil's U`_ statistic measuring the association between two categorical (nominal) data series.
.. math::
U(X|Y) = \frac{H(X) - H(X|Y)}{H(X)}
where :math:`H(X)` is entropy of variable :math:`X` while :math:`H(X|Y)` is the conditional entropy of :math:`X`
given :math:`Y`. It is also know as the Uncertainty Coefficient.
Theils's U is an asymmetric coefficient, i.e. :math:`TheilsU(preds, target) \neq TheilsU(target, preds)`.
The output values lies in [0, 1]. 0 means y has no information about x while value 1 means y has complete
information about x.
Args:
num_classes: Integer specifing 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'``
kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
Returns:
Theil's U Statistic: Tensor
Example:
>>> from torchmetrics.nominal import TheilsU
>>> _ = torch.manual_seed(42)
>>> preds = torch.randint(10, (10,))
>>> target = torch.randint(10, (10,))
>>> metric = TheilsU(num_classes=10)
>>> metric(preds, target)
tensor(0.8530)
"""
full_state_update: bool = False
is_differentiable: bool = False
higher_is_better: bool = True
plot_lower_bound: float = 0.0
plot_upper_bound: float = 1.0
confmat: Tensor
def __init__(
self,
num_classes: int,
nan_strategy: Literal["replace", "drop"] = "replace",
nan_replace_value: Optional[Union[int, float]] = 0.0,
**kwargs: Any,
) -> None:
super().__init__(**kwargs)
self.num_classes = num_classes
_nominal_input_validation(nan_strategy, nan_replace_value)
self.nan_strategy = nan_strategy
self.nan_replace_value = nan_replace_value
self.add_state("confmat", torch.zeros(num_classes, num_classes), dist_reduce_fx="sum")
def update(self, preds: Tensor, target: Tensor) -> None:
"""Update state with predictions and targets.
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)
"""
confmat = _theils_u_update(preds, target, self.num_classes, self.nan_strategy, self.nan_replace_value)
self.confmat += confmat
def compute(self) -> Tensor:
"""Compute Theil's U statistic."""
return _theils_u_compute(self.confmat)
def plot(self, val: Union[Tensor, Sequence[Tensor], None] = None, ax: Optional[_AX_TYPE] = None) -> _PLOT_OUT_TYPE:
"""Plot a single or multiple values from the metric.
Args:
val: Either a single result from calling `metric.forward` or `metric.compute` or a list of these results.
If no value is provided, will automatically call `metric.compute` and plot that result.
ax: An matplotlib axis object. If provided will add plot to that axis
Returns:
Figure and Axes object
Raises:
ModuleNotFoundError:
If `matplotlib` is not installed
.. plot::
:scale: 75
>>> # Example plotting a single value
>>> import torch
>>> from torchmetrics.nominal import TheilsU
>>> metric = TheilsU(num_classes=10)
>>> metric.update(torch.randint(10, (10,)), torch.randint(10, (10,)))
>>> fig_, ax_ = metric.plot()
.. plot::
:scale: 75
>>> # Example plotting multiple values
>>> import torch
>>> from torchmetrics.nominal import TheilsU
>>> metric = TheilsU(num_classes=10)
>>> values = [ ]
>>> for _ in range(10):
... values.append(metric(torch.randint(10, (10,)), torch.randint(10, (10,))))
>>> fig_, ax_ = metric.plot(values)
"""
return self._plot(val, ax)