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# Explained Variance¶

## Module Interface¶

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

Compute explained variance: Where is a tensor of target values, and 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:

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 (str) –

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 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])


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

## Functional Interface¶

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

Compute explained variance.

Parameters
• preds (Tensor) – estimated labels

• target (Tensor) – ground truth labels

• 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

Example

>>> from torchmetrics.functional 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])

Return type

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