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# Relative Squared Error (RSE)¶

## Module Interface¶

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

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:

Parameters:

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)[source]

Plot a single or multiple values from the metric.

Parameters:
Return type:
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)[source]

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:
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)


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