Meansquarederror

---
name: meansquarederror
description: Compute the MeanSquaredError metric — provided by torchmetrics. Use when the user has predictions and ground-truth and needs to compute MeanSquaredError, or asks how to score with MeanSquaredError.
metadata:
  skill_kind: metric
  source_lib: torchmetrics
  import_path: torchmetrics.MeanSquaredError
  source: library_introspection
---

# meansquarederror

> Metric `MeanSquaredError` from `torchmetrics` (torchmetrics.MeanSquaredError)

## When to invoke this skill

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

## Reference signature

```python
from torchmetrics import MeanSquaredError

# MeanSquaredError(squared: bool = True, num_outputs: int = 1, **kwargs: Any) -> None
```

## Library docstring

```
Compute `mean squared error`_ (MSE).

.. math:: \text{MSE} = \frac{1}{N}\sum_i^N(y_i - \hat{y_i})^2

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
- ``target`` (:class:`~torch.Tensor`): Ground truth values

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

- ``mean_squared_error`` (:class:`~torch.Tensor`): A tensor with the mean squared error

Args:
    squared: If True returns MSE value, if False returns RMSE value.
    num_outputs: Number of outputs in multioutput setting
    kwargs: Additional keyword arguments, see :ref:`Metric kwargs` 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.])
```

## Quick recipe

```python
import torchmetrics as _m
score = _m.MeanSquaredError(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)`.