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kendall.py
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kendall.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, List, Optional, Sequence, Tuple, Union
from torch import Tensor
from typing_extensions import Literal
from torchmetrics.functional.regression.kendall import (
_kendall_corrcoef_compute,
_kendall_corrcoef_update,
_MetricVariant,
_TestAlternative,
)
from torchmetrics.metric import Metric
from torchmetrics.utilities.data import dim_zero_cat
from torchmetrics.utilities.imports import _MATPLOTLIB_AVAILABLE
from torchmetrics.utilities.plot import _AX_TYPE, _PLOT_OUT_TYPE
if not _MATPLOTLIB_AVAILABLE:
__doctest_skip__ = ["KendallRankCorrCoef.plot"]
class KendallRankCorrCoef(Metric):
r"""Compute `Kendall Rank Correlation Coefficient`_.
.. math::
tau_a = \frac{C - D}{C + D}
where :math:`C` represents concordant pairs, :math:`D` stands for discordant pairs.
.. math::
tau_b = \frac{C - D}{\sqrt{(C + D + T_{preds}) * (C + D + T_{target})}}
where :math:`C` represents concordant pairs, :math:`D` stands for discordant pairs and :math:`T` represents
a total number of ties.
.. math::
tau_c = 2 * \frac{C - D}{n^2 * \frac{m - 1}{m}}
where :math:`C` represents concordant pairs, :math:`D` stands for discordant pairs, :math:`n` is a total number
of observations and :math:`m` is a ``min`` of unique values in ``preds`` and ``target`` sequence.
Definitions according to Definition according to `The Treatment of Ties in Ranking Problems`_.
As input to ``forward`` and ``update`` the metric accepts the following input:
- ``preds`` (:class:`~torch.Tensor`): Sequence of data in float tensor of either shape ``(N,)`` or ``(N,d)``
- ``target`` (:class:`~torch.Tensor`): Sequence of data in float tensor of either shape ``(N,)`` or ``(N,d)``
As output of ``forward`` and ``compute`` the metric returns the following output:
- ``kendall`` (:class:`~torch.Tensor`): A tensor with the correlation tau statistic,
and if it is not None, the p-value of corresponding statistical test.
Args:
variant: Indication of which variant of Kendall's tau to be used
t_test: Indication whether to run t-test
alternative: Alternative hypothesis for t-test. Possible values:
- 'two-sided': the rank correlation is nonzero
- 'less': the rank correlation is negative (less than zero)
- 'greater': the rank correlation is positive (greater than zero)
num_outputs: Number of outputs in multioutput setting
kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
Raises:
ValueError: If ``t_test`` is not of a type bool
ValueError: If ``t_test=True`` and ``alternative=None``
Example (single output regression):
>>> from torch import tensor
>>> from torchmetrics.regression import KendallRankCorrCoef
>>> preds = tensor([2.5, 0.0, 2, 8])
>>> target = tensor([3, -0.5, 2, 1])
>>> kendall = KendallRankCorrCoef()
>>> kendall(preds, target)
tensor(0.3333)
Example (multi output regression):
>>> from torchmetrics.regression import KendallRankCorrCoef
>>> preds = tensor([[2.5, 0.0], [2, 8]])
>>> target = tensor([[3, -0.5], [2, 1]])
>>> kendall = KendallRankCorrCoef(num_outputs=2)
>>> kendall(preds, target)
tensor([1., 1.])
Example (single output regression with t-test):
>>> from torchmetrics.regression import KendallRankCorrCoef
>>> preds = tensor([2.5, 0.0, 2, 8])
>>> target = tensor([3, -0.5, 2, 1])
>>> kendall = KendallRankCorrCoef(t_test=True, alternative='two-sided')
>>> kendall(preds, target)
(tensor(0.3333), tensor(0.4969))
Example (multi output regression with t-test):
>>> from torchmetrics.regression import KendallRankCorrCoef
>>> preds = tensor([[2.5, 0.0], [2, 8]])
>>> target = tensor([[3, -0.5], [2, 1]])
>>> kendall = KendallRankCorrCoef(t_test=True, alternative='two-sided', num_outputs=2)
>>> kendall(preds, target)
(tensor([1., 1.]), tensor([nan, nan]))
"""
is_differentiable = False
higher_is_better = None
full_state_update = True
plot_lower_bound: float = 0.0
plot_upper_bound: float = 1.0
preds: List[Tensor]
target: List[Tensor]
def __init__(
self,
variant: Literal["a", "b", "c"] = "b",
t_test: bool = False,
alternative: Optional[Literal["two-sided", "less", "greater"]] = "two-sided",
num_outputs: int = 1,
**kwargs: Any,
) -> None:
super().__init__(**kwargs)
if not isinstance(t_test, bool):
raise ValueError(f"Argument `t_test` is expected to be of a type `bool`, but got {type(t_test)}.")
if t_test and alternative is None:
raise ValueError("Argument `alternative` is required if `t_test=True` but got `None`.")
self.variant = _MetricVariant.from_str(str(variant))
self.alternative = _TestAlternative.from_str(str(alternative)) if t_test else None
self.num_outputs = num_outputs
self.add_state("preds", [], dist_reduce_fx="cat")
self.add_state("target", [], dist_reduce_fx="cat")
def update(self, preds: Tensor, target: Tensor) -> None:
"""Update variables required to compute Kendall rank correlation coefficient."""
self.preds, self.target = _kendall_corrcoef_update(
preds,
target,
self.preds,
self.target,
num_outputs=self.num_outputs,
)
def compute(self) -> Union[Tensor, Tuple[Tensor, Tensor]]:
"""Compute Kendall rank correlation coefficient, and optionally p-value of corresponding statistical test."""
preds = dim_zero_cat(self.preds)
target = dim_zero_cat(self.target)
tau, p_value = _kendall_corrcoef_compute(
preds, target, self.variant, self.alternative # type: ignore[arg-type] # todo
)
if p_value is not None:
return tau, p_value
return tau
def plot(
self, val: Optional[Union[Tensor, Sequence[Tensor]]] = 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
>>> from torch import randn
>>> # Example plotting a single value
>>> from torchmetrics.regression import KendallRankCorrCoef
>>> metric = KendallRankCorrCoef()
>>> metric.update(randn(10,), randn(10,))
>>> fig_, ax_ = metric.plot()
.. plot::
:scale: 75
>>> from torch import randn
>>> # Example plotting multiple values
>>> from torchmetrics.regression import KendallRankCorrCoef
>>> metric = KendallRankCorrCoef()
>>> values = []
>>> for _ in range(10):
... values.append(metric(randn(10,), randn(10,)))
>>> fig, ax = metric.plot(values)
"""
return self._plot(val, ax)