Tschuprow’s T

Module Interface

class torchmetrics.nominal.TschuprowsT(num_classes, bias_correction=True, nan_strategy='replace', nan_replace_value=0.0, **kwargs)[source]

Compute Tschuprow’s T statistic measuring the association between two categorical (nominal) data series.

$T = \sqrt{\frac{\chi^2 / n}{\sqrt{(r - 1) * (k - 1)}}}$

where

$\chi^2 = \sum_{i,j} \ frac{\left(n_{ij} - \frac{n_{i.} n_{.j}}{n}\right)^2}{\frac{n_{i.} n_{.j}}{n}}$

where $n_{ij}$ denotes the number of times the values $(A_i, B_j)$ are observed with $A_i, B_j$ represent frequencies of values in preds and target, respectively.

Tschuprow’s T is a symmetric coefficient, i.e. $T(preds, target) = T(target, preds)$ .

The output values lies in [0, 1] with 1 meaning the perfect association.

Parameters:

num_classes (int) – Integer specifing the number of classes
bias_correction (bool) – Indication of whether to use bias correction.
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.

Returns:

Tschuprow’s T statistic

Raises:

ValueError – If nan_strategy is not one of ‘replace’ and ‘drop’
ValueError – If nan_strategy is equal to ‘replace’ and nan_replace_value is not an int or float

Example

>>>>>> from torchmetrics.nominal import TschuprowsT
>>> _ = torch.manual_seed(42)
>>> preds = torch.randint(0, 4, (100,))
>>> target = torch.round(preds + torch.randn(100)).clamp(0, 4)
>>> tschuprows_t = TschuprowsT(num_classes=5)
>>> tschuprows_t(preds, target)
tensor(0.4930)

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 TschuprowsT
>>> metric = TschuprowsT(num_classes=5)
>>> metric.update(torch.randint(0, 4, (100,)), torch.randint(0, 4, (100,)))
>>> fig_, ax_ = metric.plot()

>>>>>> # Example plotting multiple values
>>> import torch
>>> from torchmetrics.nominal import TschuprowsT
>>> metric = TschuprowsT(num_classes=5)
>>> values = [ ]
>>> for _ in range(10):
...     values.append(metric(torch.randint(0, 4, (100,)), torch.randint(0, 4, (100,))))
>>> fig_, ax_ = metric.plot(values)

Functional Interface

torchmetrics.functional.nominal.tschuprows_t(preds, target, bias_correction=True, nan_strategy='replace', nan_replace_value=0.0)[source]

Compute Tschuprow’s T statistic measuring the association between two categorical (nominal) data series.

$T = \sqrt{\frac{\chi^2 / n}{\sqrt{(r - 1) * (k - 1)}}}$

where

$\chi^2 = \sum_{i,j} \ frac{\left(n_{ij} - \frac{n_{i.} n_{.j}}{n}\right)^2}{\frac{n_{i.} n_{.j}}{n}}$

where $n_{ij}$ denotes the number of times the values $(A_i, B_j)$ are observed with $A_i, B_j$ represent frequencies of values in preds and target, respectively.

Tschuprow’s T is a symmetric coefficient, i.e. $T(preds, target) = T(target, preds)$ .

The output values lies in [0, 1] with 1 meaning the perfect association.

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)
bias_correction (bool) – Indication of whether to use bias correction.
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:

Tschuprow’s T statistic

Example

>>>>>> from torchmetrics.functional.nominal import tschuprows_t
>>> _ = torch.manual_seed(42)
>>> preds = torch.randint(0, 4, (100,))
>>> target = torch.round(preds + torch.randn(100)).clamp(0, 4)
>>> tschuprows_t(preds, target)
tensor(0.4930)

tschuprows_t_matrix

torchmetrics.functional.nominal.tschuprows_t_matrix(matrix, bias_correction=True, nan_strategy='replace', nan_replace_value=0.0)[source]

Compute Tschuprow’s T statistic between a set of multiple variables.

This can serve as a convenient tool to compute Tschuprow’s T 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
bias_correction (bool) – Indication of whether to use bias correction.
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:

Tschuprow’s T statistic for a dataset of categorical variables

Example

>>>>>> from torchmetrics.functional.nominal import tschuprows_t_matrix
>>> _ = torch.manual_seed(42)
>>> matrix = torch.randint(0, 4, (200, 5))
>>> tschuprows_t_matrix(matrix)
tensor([[1.0000, 0.0637, 0.0000, 0.0542, 0.1337],
        [0.0637, 1.0000, 0.0000, 0.0000, 0.0000],
        [0.0000, 0.0000, 1.0000, 0.0000, 0.0649],
        [0.0542, 0.0000, 0.0000, 1.0000, 0.1100],
        [0.1337, 0.0000, 0.0649, 0.1100, 1.0000]])