Explainedvariance

explainedvariance

Metric ExplainedVariance from torchmetrics (torchmetrics.ExplainedVariance)

When to invoke this skill

The user has predictions + ground truth and asks to evaluate with ExplainedVariance, or mentions torchmetrics.ExplainedVariance directly, or wants the standard torchmetrics implementation.

Reference signature

from torchmetrics import ExplainedVariance

# ExplainedVariance(multioutput: Literal['raw_values', 'uniform_average', 'variance_weighted'] = 'uniform_average', **kwargs: Any) -> None

Library docstring

Compute `explained variance`_.

.. math:: \text{ExplainedVariance} = 1 - \frac{\text{Var}(y - \hat{y})}{\text{Var}(y)}

Where :math:`y` is a tensor of target values, and :math:`\hat{y}` is a tensor of predictions.

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

- ``preds`` (:class:`~torch.Tensor`): Predictions from model in float tensor
  with shape ``(N,)`` or ``(N, ...)`` (multioutput)
- ``target`` (:class:`~torch.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`` (:class:`~torch.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.

Args:
    multioutput:
        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: Additional keyword arguments, see :ref:`Metric kwargs` 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])

Quick recipe

import torchmetrics as _m
score = _m.ExplainedVariance(y_true, y_pred)

Don'ts

• Don't reimplement when the library version handles edge cases (NaN, ties, empty inputs) better than a hand-rolled formula.
• Always check the library version's argument order — sklearn is (y_true, y_pred) while torchmetrics is (preds, target).