R2 Score¶

Module Interface¶

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

Computes 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 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])

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

Functional Interface¶

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