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# Concordance Corr. Coef.¶

## Module Interface¶

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

Compute concordance correlation coefficient that measures the agreement between two variables.

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

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.regression import ConcordanceCorrCoef
>>> from torch import tensor
>>> target = tensor([3, -0.5, 2, 7])
>>> preds = tensor([2.5, 0.0, 2, 8])
>>> concordance = ConcordanceCorrCoef()
>>> concordance(preds, target)
tensor(0.9777)

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

plot(val=None, ax=None)[source]

Plot a single or multiple values from the metric.

Parameters:
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 ConcordanceCorrCoef
>>> metric = ConcordanceCorrCoef()
>>> metric.update(randn(10,), randn(10,))
>>> fig_, ax_ = metric.plot()

>>> from torch import randn
>>> # Example plotting multiple values
>>> from torchmetrics.regression import ConcordanceCorrCoef
>>> metric = ConcordanceCorrCoef()
>>> values = []
>>> for _ in range(10):
...     values.append(metric(randn(10,), randn(10,)))
>>> fig, ax = metric.plot(values)


## Functional Interface¶

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

Compute concordance correlation coefficient that measures the agreement between two variables.

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

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:
Return type:

Tensor

Example (single output regression):
>>> from torchmetrics.functional.regression 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.regression 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])


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