Kendall Rank Corr. Coef.¶

Module Interface¶

class torchmetrics.KendallRankCorrCoef(variant='b', t_test=False, alternative='two-sided', num_outputs=1, **kwargs)[source]

Computes Kendall Rank Correlation Coefficient:

$tau_a = \frac{C - D}{C + D}$

where $C$ represents concordant pairs, $D$ stands for discordant pairs.

$tau_b = \frac{C - D}{\sqrt{(C + D + T_{preds}) * (C + D + T_{target})}}$

where $C$ represents concordant pairs, $D$ stands for discordant pairs and $T$ represents a total number of ties.

$tau_c = 2 * \frac{C - D}{n^2 * \frac{m - 1}{m}}$

where $C$ represents concordant pairs, $D$ stands for discordant pairs, $n$ is a total number of observations and $m$ 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 (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 and compute 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 used
t_test¶ (bool) – Indication whether to run t-test
alternative¶ (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 setting
kwargs¶ (Any) – Additional keyword arguments, see Advanced metric settings 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):

>>> import torch
>>> from torchmetrics.regression import KendallRankCorrCoef
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> target = torch.tensor([3, -0.5, 2, 1])
>>> kendall = KendallRankCorrCoef()
>>> kendall(preds, target)
tensor(0.3333)

Example (multi output regression):

>>> import torch
>>> from torchmetrics.regression import KendallRankCorrCoef
>>> preds = torch.tensor([[2.5, 0.0], [2, 8]])
>>> target = torch.tensor([[3, -0.5], [2, 1]])
>>> kendall = KendallRankCorrCoef(num_outputs=2)
>>> kendall(preds, target)
tensor([1., 1.])

Example (single output regression with t-test):

>>> import torch
>>> from torchmetrics.regression import KendallRankCorrCoef
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> target = torch.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):

>>> import torch
>>> from torchmetrics.regression import KendallRankCorrCoef
>>> preds = torch.tensor([[2.5, 0.0], [2, 8]])
>>> target = torch.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]))

Initializes internal Module state, shared by both nn.Module and ScriptModule.

Functional Interface¶

torchmetrics.functional.kendall_rank_corrcoef(preds, target, variant='b', t_test=False, alternative='two-sided')[source]

Computes Kendall Rank Correlation Coefficient.