Relativesquarederror

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

# relativesquarederror

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

## When to invoke this skill

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

## Reference signature

```python
from torchmetrics import RelativeSquaredError

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

## Library docstring

```
Computes the relative squared error (RSE).

.. math:: \text{RSE} = \frac{\sum_i^N(y_i - \hat{y_i})^2}{\sum_i^N(y_i - \overline{y})^2}

Where :math:`y` is a tensor of target values with mean :math:`\overline{y}`, and
:math:`\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`` (:class:`~torch.Tensor`): Predictions from model in float tensor with shape ``(N,)``
  or ``(N, M)`` (multioutput)
- ``target`` (:class:`~torch.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`` (:class:`~torch.Tensor`): A tensor with the RSE score(s)

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

## Quick recipe

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