Relative Squared Error (RSE)

Module Interface

class torchmetrics.RelativeSquaredError(num_outputs=1, squared=True, **kwargs)

Computes the relative squared error (RSE).

\[\text{RSE} = \frac{\sum_i^N(y_i - \hat{y_i})^2}{\sum_i^N(y_i - \overline{y})^2}\]

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

If num_outputs > 1, the returned value is averaged over all the outputs.

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:

• rse (Tensor): A tensor with the RSE score(s)

Parameters:

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

• squared (bool) – If True returns RSE value, if False returns RRSE value.

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

Example

>>> from torchmetrics.regression import RelativeSquaredError
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> relative_squared_error = RelativeSquaredError()
>>> relative_squared_error(preds, target)
tensor(0.0514)

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

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

Functional Interface

torchmetrics.functional.relative_squared_error(preds, target, squared=True)

Computes the relative squared error (RSE).

\[\text{RSE} = \frac{\sum_i^N(y_i - \hat{y_i})^2}{\sum_i^N(y_i - \overline{y})^2}\]

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

If preds and targets are 2D tensors, the RSE is averaged over the second dim.

Parameters:

• preds (Tensor) – estimated labels

• target (Tensor) – ground truth labels

• squared (bool) – returns RRSE value if set to False

Return type:

Tensor

Returns:

Tensor with RSE

Example

>>> from torchmetrics.functional.regression import relative_squared_error
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> relative_squared_error(preds, target)
tensor(0.0514)