Mean Squared Error (MSE)

Module Interface

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

Compute mean squared error (MSE).

\[\text{MSE} = \frac{1}{N}\sum_i^N(y_i - \hat{y_i})^2\]

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

• target (Tensor): Ground truth values

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

• mean_squared_error (Tensor): A tensor with the mean squared error

Parameters:

• squared (bool) – If True returns MSE value, if False returns RMSE value.

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

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

Example::

Single output mse computation:

>>> from torch import tensor
>>> from torchmetrics.regression import MeanSquaredError
>>> target = tensor([2.5, 5.0, 4.0, 8.0])
>>> preds = tensor([3.0, 5.0, 2.5, 7.0])
>>> mean_squared_error = MeanSquaredError()
>>> mean_squared_error(preds, target)
tensor(0.8750)

Example::

Multioutput mse computation:

>>> from torch import tensor
>>> from torchmetrics.regression import MeanSquaredError
>>> target = tensor([[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]])
>>> preds = tensor([[1.0, 2.0, 3.0], [1.0, 2.0, 3.0]])
>>> mean_squared_error = MeanSquaredError(num_outputs=3)
>>> mean_squared_error(preds, target)
tensor([1., 4., 9.])

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

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

Functional Interface

torchmetrics.functional.mean_squared_error(preds, target, squared=True, num_outputs=1)

Compute mean squared error.

Parameters:

• preds (Tensor) – estimated labels

• target (Tensor) – ground truth labels

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

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

Return type:

Tensor

Returns:

Tensor with MSE

Example

>>> from torchmetrics.functional.regression import mean_squared_error
>>> x = torch.tensor([0., 1, 2, 3])
>>> y = torch.tensor([0., 1, 2, 2])
>>> mean_squared_error(x, y)
tensor(0.2500)