Theil’s U¶

Module Interface¶

class torchmetrics.nominal.TheilsU(num_classes, nan_strategy='replace', nan_replace_value=0.0, **kwargs)[source]¶

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

\[U(X|Y) = \frac{H(X) - H(X|Y)}{H(X)}\]

where \(H(X)\) is entropy of variable \(X\) while \(H(X|Y)\) is the conditional entropy of \(X\) given \(Y\). It is also know as the Uncertainty Coefficient. Theils’s U is an asymmetric coefficient, i.e. \(TheilsU(preds, target) \neq TheilsU(target, preds)\), 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 (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 (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 (Tensor): Scalar tensor containing the Theil’s U statistic.

Parameters:

num_classes¶ (int) – Integer specifing the number of classes
nan_strategy¶ (Literal['replace', 'drop']) – Indication of whether to replace or drop NaN values
nan_replace_value¶ (Union[int, float, None]) – Value to replace NaN``s when ``nan_strategy = 'replace'
kwargs¶ (Any) – Additional keyword arguments, see Advanced metric settings for more info.

Example:

>>> from torchmetrics.nominal import TheilsU
>>> _ = torch.manual_seed(42)
>>> preds = torch.randint(10, (10,))
>>> target = torch.randint(10, (10,))
>>> metric = TheilsU(num_classes=10)
>>> metric(preds, target)
tensor(0.8530)

plot(val=None, ax=None)[source]¶

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

>>> # Example plotting a single value
>>> import torch
>>> from torchmetrics.nominal import TheilsU
>>> metric = TheilsU(num_classes=10)
>>> metric.update(torch.randint(10, (10,)), torch.randint(10, (10,)))
>>> fig_, ax_ = metric.plot()

>>> # Example plotting multiple values
>>> import torch
>>> from torchmetrics.nominal import TheilsU
>>> metric = TheilsU(num_classes=10)
>>> values = [ ]
>>> for _ in range(10):
...     values.append(metric(torch.randint(10, (10,)), torch.randint(10, (10,))))
>>> fig_, ax_ = metric.plot(values)

Functional Interface¶

torchmetrics.functional.nominal.theils_u(preds, target, nan_strategy='replace', nan_replace_value=0.0)[source]¶

Compute Theils Uncertainty coefficient statistic measuring the association between two nominal data series.

\[U(X|Y) = \frac{H(X) - H(X|Y)}{H(X)}\]

where \(H(X)\) is entropy of variable \(X\) while \(H(X|Y)\) is the conditional entropy of \(X\) given \(Y\).

Theils’s U is an asymmetric coefficient, i.e. \(TheilsU(preds, target) \neq TheilsU(target, preds)\).

The output values lies in [0, 1]. 0 means y has no information about x while value 1 means y has complete information about x.

Parameters:

preds¶ (Tensor) – 1D or 2D tensor of categorical (nominal) data - 1D shape: (batch_size,) - 2D shape: (batch_size, num_classes)
target¶ (Tensor) – 1D or 2D tensor of categorical (nominal) data - 1D shape: (batch_size,) - 2D shape: (batch_size, num_classes)
nan_strategy¶ (Literal['replace', 'drop']) – Indication of whether to replace or drop NaN values
nan_replace_value¶ (Union[int, float, None]) – Value to replace NaN``s when ``nan_strategy = 'replace'

Return type:

Tensor

Returns:

Tensor containing Theil’s U statistic

Example

>>> from torchmetrics.functional.nominal import theils_u
>>> _ = torch.manual_seed(42)
>>> preds = torch.randint(10, (10,))
>>> target = torch.randint(10, (10,))
>>> theils_u(preds, target)
tensor(0.8530)

theils_u_matrix¶

torchmetrics.functional.nominal.theils_u_matrix(matrix, nan_strategy='replace', nan_replace_value=0.0)[source]¶

Compute Theil’s U statistic between a set of multiple variables.

This can serve as a convenient tool to compute Theil’s U statistic for analyses of correlation between categorical variables in your dataset.

Parameters:

matrix¶ (Tensor) – A tensor of categorical (nominal) data, where: - rows represent a number of data points - columns represent a number of categorical (nominal) features
nan_strategy¶ (Literal['replace', 'drop']) – Indication of whether to replace or drop NaN values
nan_replace_value¶ (Union[int, float, None]) – Value to replace NaN``s when ``nan_strategy = 'replace'

Return type:

Tensor

Returns:

Theil’s U statistic for a dataset of categorical variables

Example

>>> from torchmetrics.functional.nominal import theils_u_matrix
>>> _ = torch.manual_seed(42)
>>> matrix = torch.randint(0, 4, (200, 5))
>>> theils_u_matrix(matrix)
tensor([[1.0000, 0.0202, 0.0142, 0.0196, 0.0353],
        [0.0202, 1.0000, 0.0070, 0.0136, 0.0065],
        [0.0143, 0.0070, 1.0000, 0.0125, 0.0206],
        [0.0198, 0.0137, 0.0125, 1.0000, 0.0312],
        [0.0352, 0.0065, 0.0204, 0.0308, 1.0000]])