Kendall Rank Corr. Coef.¶
Module Interface¶
- class torchmetrics.KendallRankCorrCoef(variant='b', t_test=False, alternative='two-sided', num_outputs=1, **kwargs)[source]
Compute Kendall Rank Correlation Coefficient.
where
represents concordant pairs,
stands for discordant pairs.
where
represents concordant pairs,
stands for discordant pairs and
represents a total number of ties.
where
represents concordant pairs,
stands for discordant pairs,
is a total number of observations and
is a
min
of unique values inpreds
andtarget
sequence.Definitions according to Definition according to The Treatment of Ties in Ranking Problems.
As input to
forward
andupdate
the metric accepts the following input:preds
(Tensor
): Sequence of data in float tensor of either shape(N,)
or(N,d)
target
(Tensor
): Sequence of data in float tensor of either shape(N,)
or(N,d)
As output of
forward
andcompute
the metric returns the following output:kendall
(Tensor
): A tensor with the correlation tau statistic, and if it is not None, the p-value of corresponding statistical test.
- Parameters:
variant¶ (
Literal
['a'
,'b'
,'c'
]) – Indication of which variant of Kendall’s tau to be usedalternative¶ (
Optional
[Literal
['two-sided'
,'less'
,'greater'
]]) – 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¶ (
int
) – Number of outputs in multioutput settingkwargs¶ (
Any
) – Additional keyword arguments, see Advanced metric settings for more info.
- Raises:
ValueError – If
t_test
is not of a type boolValueError – If
t_test=True
andalternative=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]))
- plot(val=None, ax=None)[source]
Plot a single or multiple values from the metric.
- Parameters:
val¶ (
Union
[Tensor
,Sequence
[Tensor
],None
]) – 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¶ (
Optional
[Axes
]) – An matplotlib axis object. If provided will add plot to that axis
- Return type:
- Returns:
Figure and Axes object
- Raises:
ModuleNotFoundError – If matplotlib is not installed
>>> 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()
>>> 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)
Functional Interface¶
- torchmetrics.functional.kendall_rank_corrcoef(preds, target, variant='b', t_test=False, alternative='two-sided')[source]
Compute Kendall Rank Correlation Coefficient.
where
represents concordant pairs,
stands for discordant pairs.
where
represents concordant pairs,
stands for discordant pairs and
represents a total number of ties.
where
represents concordant pairs,
stands for discordant pairs,
is a total number of observations and
is a
min
of unique values inpreds
andtarget
sequence.Definitions according to Definition according to The Treatment of Ties in Ranking Problems.
- Parameters:
preds¶ (
Tensor
) – Sequence of data of either shape(N,)
or(N,d)
target¶ (
Tensor
) – Sequence of data of either shape(N,)
or(N,d)
variant¶ (
Literal
['a'
,'b'
,'c'
]) – Indication of which variant of Kendall’s tau to be usedalternative¶ (
Optional
[Literal
['two-sided'
,'less'
,'greater'
]]) – 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)
- Return type:
- Returns:
Correlation tau statistic (Optional) p-value of corresponding statistical test (asymptotic)
- Raises:
ValueError – If
t_test
is not of a type boolValueError – If
t_test=True
andalternative=None
- Example (single output regression):
>>> from torchmetrics.functional.regression import kendall_rank_corrcoef >>> preds = torch.tensor([2.5, 0.0, 2, 8]) >>> target = torch.tensor([3, -0.5, 2, 1]) >>> kendall_rank_corrcoef(preds, target) tensor(0.3333)
- Example (multi output regression):
>>> from torchmetrics.functional.regression import kendall_rank_corrcoef >>> preds = torch.tensor([[2.5, 0.0], [2, 8]]) >>> target = torch.tensor([[3, -0.5], [2, 1]]) >>> kendall_rank_corrcoef(preds, target) tensor([1., 1.])
- Example (single output regression with t-test)
>>> from torchmetrics.functional.regression import kendall_rank_corrcoef >>> preds = torch.tensor([2.5, 0.0, 2, 8]) >>> target = torch.tensor([3, -0.5, 2, 1]) >>> kendall_rank_corrcoef(preds, target, t_test=True, alternative='two-sided') (tensor(0.3333), tensor(0.4969))
- Example (multi output regression with t-test):
>>> from torchmetrics.functional.regression import kendall_rank_corrcoef >>> preds = torch.tensor([[2.5, 0.0], [2, 8]]) >>> target = torch.tensor([[3, -0.5], [2, 1]]) >>> kendall_rank_corrcoef(preds, target, t_test=True, alternative='two-sided') (tensor([1., 1.]), tensor([nan, nan]))