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Concordance Corr. Coef.

Module Interface

class torchmetrics.ConcordanceCorrCoef(num_outputs=1, **kwargs)[source]

Computes concordance correlation coefficient that measures the agreement between two variables. It is defined as.

\rho_c = \frac{2 \rho \sigma_x \sigma_y}{\sigma_x^2 + \sigma_y^2 + (\mu_x - \mu_y)^2}

where \mu_x, \mu_y is the means for the two variables, \sigma_x^2, \sigma_y^2 are the corresponding variances and rho is the pearson correlation coefficient between the two variables.

As input to forward and update the metric accepts the following input:

  • preds (Tensor): either single output float tensor with shape (N,) or multioutput float tensor of shape (N,d)

  • target (Tensor): either single output float tensor with shape (N,) or multioutput float tensor of shape (N,d)

As output of forward and compute the metric returns the following output:

  • concordance (Tensor): A scalar float tensor with the concordance coefficient(s) for non-multioutput input or a float tensor with shape (d,) for multioutput input

Parameters
Example (single output regression):
>>> from torchmetrics import ConcordanceCorrCoef
>>> import torch
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> concordance = ConcordanceCorrCoef()
>>> concordance(preds, target)
tensor(0.9777)
Example (multi output regression):
>>> from torchmetrics import ConcordanceCorrCoef
>>> import torch
>>> target = torch.tensor([[3, -0.5], [2, 7]])
>>> preds = torch.tensor([[2.5, 0.0], [2, 8]])
>>> concordance = ConcordanceCorrCoef(num_outputs=2)
>>> concordance(preds, target)
tensor([0.7273, 0.9887])

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

Functional Interface

torchmetrics.functional.concordance_corrcoef(preds, target)[source]

Computes concordance correlation coefficient that measures the agreement between two variables. It is defined as.

\rho_c = \frac{2 \rho \sigma_x \sigma_y}{\sigma_x^2 + \sigma_y^2 + (\mu_x - \mu_y)^2}

where \mu_x, \mu_y is the means for the two variables, \sigma_x^2, \sigma_y^2 are the corresponding variances and rho is the pearson correlation coefficient between the two variables.

Parameters
  • preds (Tensor) – estimated scores

  • target (Tensor) – ground truth scores

Example (single output regression):
>>> from torchmetrics.functional import concordance_corrcoef
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> concordance_corrcoef(preds, target)
tensor([0.9777])
Example (multi output regression):
>>> from torchmetrics.functional import concordance_corrcoef
>>> target = torch.tensor([[3, -0.5], [2, 7]])
>>> preds = torch.tensor([[2.5, 0.0], [2, 8]])
>>> concordance_corrcoef(preds, target)
tensor([0.7273, 0.9887])
Return type

Tensor

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