# Mean Absolute Error (MAE)¶

## Module Interface¶

class torchmetrics.MeanAbsoluteError(num_outputs=1, **kwargs)[source]
$\text{MAE} = \frac{1}{N}\sum_i^N | y_i - \hat{y_i} |$

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:

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

• mean_absolute_error (Tensor): A tensor with the mean absolute error over the state

Parameters:

Example

>>> from torch import tensor
>>> from torchmetrics.regression import MeanAbsoluteError
>>> target = tensor([3.0, -0.5, 2.0, 7.0])
>>> preds = tensor([2.5, 0.0, 2.0, 8.0])
>>> mean_absolute_error = MeanAbsoluteError()
>>> mean_absolute_error(preds, target)
tensor(0.5000)

Example::

Multioutput mse computation:

>>> from torch import tensor
>>> from torchmetrics.regression import MeanAbsoluteError
>>> 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_absolute_error = MeanAbsoluteError(num_outputs=3)
>>> mean_absolute_error(preds, target)
tensor([1., 2., 3.])

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

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


## Functional Interface¶

torchmetrics.functional.mean_absolute_error(preds, target, num_outputs=1)[source]

Compute mean absolute error.

Parameters:
Return type:

Tensor

Returns:

Tensor with MAE

Example

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