theilsu

Metric TheilsU from torchmetrics (torchmetrics.TheilsU)

When to invoke this skill

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

Reference signature

from torchmetrics import TheilsU

# TheilsU(num_classes: int, nan_strategy: Literal['replace', 'drop'] = 'replace', nan_replace_value: Optional[float] = 0.0, **kwargs: Any) -> None

Library docstring

Compute `Theil's U`_ statistic measuring the association between two categorical (nominal) data series.

.. math::
    U(X|Y) = \frac{H(X) - H(X|Y)}{H(X)}

where :math:`H(X)` is entropy of variable :math:`X` while :math:`H(X|Y)` is the conditional entropy of :math:`X`
given :math:`Y`. It is also know as the Uncertainty Coefficient. Theils's U is an asymmetric coefficient, i.e.
:math:`TheilsU(preds, target) \neq TheilsU(target, preds)`, so the order of the inputs matters. The output values
lies in [0, 1], where a 0 means y has no information about x while value 1 means y has complete information about x.

As input to ``forward`` and ``update`` the metric accepts the following input:

- ``preds`` (:class:`~torch.Tensor`): Either 1D or 2D tensor of categorical (nominal) data from the first data
  series (called X in the above definition) with shape ``(batch_size,)`` or ``(batch_size, num_classes)``,
  respectively.
- ``target`` (:class:`~torch.Tensor`): Either 1D or 2D tensor of categorical (nominal) data from the second data
  series (called Y in the above definition) with shape ``(batch_size,)`` or ``(batch_size, num_classes)``,
  respectively.

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

- ``theils_u`` (:class:`~torch.Tensor`): Scalar tensor containing the Theil's U statistic.

Args:
    num_classes: Integer specifying the number of classes
    nan_strategy: Indication of whether to replace or drop ``NaN`` values
    nan_replace_value: Value to replace ``NaN``s when ``nan_strategy = 'replace'``
    kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.

Example::

    >>> from torch import randint
    >>> from torchmetrics.nominal import TheilsU
    >>> preds = randint(10, (10,))
    >>> target = randint(10, (10,))
    >>> metric = TheilsU(num_classes=10)
    >>> metric(preds, target)
    tensor(0.8530)

Quick recipe

import torchmetrics as _m
score = _m.TheilsU(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).