Explained Variance

Module Interface

class torchmetrics.ExplainedVariance(multioutput='uniform_average', **kwargs)

Compute explained variance.

\[\text{ExplainedVariance} = 1 - \frac{\text{Var}(y - \hat{y})}{\text{Var}(y)}\]

Where \(y\) is a tensor of target values, and \(\hat{y}\) is a tensor of predictions.

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, ...) (multioutput)

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

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

• explained_variance (Tensor): A tensor with the explained variance(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:

• multioutput (Literal['raw_values', 'uniform_average', 'variance_weighted']) –

  Defines aggregation in the case of multiple output scores. Can be one of the following strings (default is 'uniform_average'.):

  • '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 multioutput is not one of "raw_values", "uniform_average" or "variance_weighted".

Example

>>> from torch import tensor
>>> from torchmetrics.regression import ExplainedVariance
>>> target = tensor([3, -0.5, 2, 7])
>>> preds = tensor([2.5, 0.0, 2, 8])
>>> explained_variance = ExplainedVariance()
>>> explained_variance(preds, target)
tensor(0.9572)

>>> target = tensor([[0.5, 1], [-1, 1], [7, -6]])
>>> preds = tensor([[0, 2], [-1, 2], [8, -5]])
>>> explained_variance = ExplainedVariance(multioutput='raw_values')
>>> explained_variance(preds, target)
tensor([0.9677, 1.0000])

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

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

Functional Interface

torchmetrics.functional.explained_variance(preds, target, multioutput='uniform_average')

Compute explained variance.

Parameters:

• preds (Tensor) – estimated labels

• target (Tensor) – ground truth labels

• multioutput (Literal['raw_values', 'uniform_average', 'variance_weighted']) –

  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

Return type:

Union[Tensor, Sequence[Tensor]]

Example

>>> from torchmetrics.functional.regression import explained_variance
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> explained_variance(preds, target)
tensor(0.9572)

>>> target = torch.tensor([[0.5, 1], [-1, 1], [7, -6]])
>>> preds = torch.tensor([[0, 2], [-1, 2], [8, -5]])
>>> explained_variance(preds, target, multioutput='raw_values')
tensor([0.9677, 1.0000])