R2 Score

Module Interface

class torchmetrics.R2Score(num_outputs=1, adjusted=0, multioutput='uniform_average', **kwargs)

Compute r2 score also known as R2 Score_Coefficient Determination.

\[R^2 = 1 - \frac{SS_{res}}{SS_{tot}}\]

where \(SS_{res}=\sum_i (y_i - f(x_i))^2\) is the sum of residual squares, and \(SS_{tot}=\sum_i (y_i - \bar{y})^2\) is total sum of squares. Can also calculate adjusted r2 score given by

\[R^2_{adj} = 1 - \frac{(1-R^2)(n-1)}{n-k-1}\]

where the parameter \(k\) (the number of independent regressors) should be provided as the adjusted argument. The score is only proper defined when \(SS_{tot}\neq 0\), which can happen for near constant targets. In this case a score of 0 is returned. By definition the score is bounded between 0 and 1, where 1 corresponds to the predictions exactly matching the targets.

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

• preds (Tensor): Predictions from model in float tensor with shape (N,) or (N, M) (multioutput)

• target (Tensor): Ground truth values in float tensor with shape (N,) or (N, M) (multioutput)

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

• r2score (Tensor): A tensor with the r2 score(s)

In the case of multioutput, as default the variances will be uniformly averaged over the additional dimensions. Please see argument multioutput for changing this behavior.

Parameters:

• num_outputs (int) – Number of outputs in multioutput setting

• adjusted (int) – number of independent regressors for calculating adjusted r2 score.

• multioutput (str) –

  Defines aggregation in the case of multiple output scores. Can be one of the following strings:

  • 'raw_values' returns full set of scores

  • 'uniform_average' scores are uniformly averaged

  • 'variance_weighted' scores are weighted by their individual variances

• kwargs (Any) – Additional keyword arguments, see Advanced metric settings for more info.

Raises:

• ValueError – If adjusted parameter is not an integer larger or equal to 0.

• ValueError – If multioutput is not one of "raw_values", "uniform_average" or "variance_weighted".

Example

>>> from torchmetrics.regression import R2Score
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> r2score = R2Score()
>>> r2score(preds, target)
tensor(0.9486)

>>> target = torch.tensor([[0.5, 1], [-1, 1], [7, -6]])
>>> preds = torch.tensor([[0, 2], [-1, 2], [8, -5]])
>>> r2score = R2Score(num_outputs=2, multioutput='raw_values')
>>> r2score(preds, target)
tensor([0.9654, 0.9082])

plot(val=None, ax=None)

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:

Tuple[Figure, Union[Axes, ndarray]]

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 R2Score
>>> metric = R2Score()
>>> metric.update(randn(10,), randn(10,))
>>> fig_, ax_ = metric.plot()

>>> from torch import randn
>>> # Example plotting multiple values
>>> from torchmetrics.regression import R2Score
>>> metric = R2Score()
>>> values = []
>>> for _ in range(10):
...     values.append(metric(randn(10,), randn(10,)))
>>> fig, ax = metric.plot(values)

Functional Interface

torchmetrics.functional.r2_score(preds, target, adjusted=0, multioutput='uniform_average')

Compute r2 score also known as R2 Score_Coefficient Determination.

\[R^2 = 1 - \frac{SS_{res}}{SS_{tot}}\]

where \(SS_{res}=\sum_i (y_i - f(x_i))^2\) is the sum of residual squares, and \(SS_{tot}=\sum_i (y_i - \bar{y})^2\) is total sum of squares. Can also calculate adjusted r2 score given by

\[R^2_{adj} = 1 - \frac{(1-R^2)(n-1)}{n-k-1}\]

where the parameter \(k\) (the number of independent regressors) should be provided as the adjusted argument.

Parameters:

• preds (Tensor) – estimated labels

• target (Tensor) – ground truth labels

• adjusted (int) – number of independent regressors for calculating adjusted r2 score.

• multioutput (str) –

  Defines aggregation in the case of multiple output scores. Can be one of the following strings:

  • 'raw_values' returns full set of scores

  • 'uniform_average' scores are uniformly averaged

  • 'variance_weighted' scores are weighted by their individual variances

Raises:

• ValueError – If both preds and targets are not 1D or 2D tensors.

• ValueError – If len(preds) is less than 2 since at least 2 samples are needed to calculate r2 score.

• ValueError – If multioutput is not one of raw_values, uniform_average or variance_weighted.

• ValueError – If adjusted is not an integer greater than 0.

Return type:

Tensor

Example

>>> from torchmetrics.functional.regression import r2_score
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> r2_score(preds, target)
tensor(0.9486)

>>> target = torch.tensor([[0.5, 1], [-1, 1], [7, -6]])
>>> preds = torch.tensor([[0, 2], [-1, 2], [8, -5]])
>>> r2_score(preds, target, multioutput='raw_values')
tensor([0.9654, 0.9082])