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# Cramer’s V¶

## Module Interface¶

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

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

$V = \sqrt{\frac{\chi^2 / n}{\min(r - 1, k - 1)}}$

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. Cramer’s V is a symmetric coefficient, i.e. $$V(preds, target) = V(target, preds)$$, so order of input arguments does not matter. The output values lies in [0, 1] with 1 meaning the perfect association.

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 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 with shape (batch_size,) or (batch_size, num_classes), respectively.

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

• cramers_v (Tensor): Scalar tensor containing the Cramer’s V statistic.

Parameters:
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 CramersV
>>> _ = torch.manual_seed(42)
>>> preds = torch.randint(0, 4, (100,))
>>> target = torch.round(preds + torch.randn(100)).clamp(0, 4)
>>> cramers_v = CramersV(num_classes=5)
>>> cramers_v(preds, target)
tensor(0.5284)

plot(val=None, ax=None)[source]

Plot a single or multiple values from the metric.

Parameters:
Return type:
Returns:

Figure and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

>>> # Example plotting a single value
>>> import torch
>>> from torchmetrics.nominal import CramersV
>>> metric = CramersV(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 CramersV
>>> metric = CramersV(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.cramers_v(preds, target, bias_correction=True, nan_strategy='replace', nan_replace_value=0.0)[source]

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

$V = \sqrt{\frac{\chi^2 / n}{\min(r - 1, k - 1)}}$

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.

Cramer’s V is a symmetric coefficient, i.e. $$V(preds, target) = V(target, preds)$$.

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

Parameters:
Return type:

Tensor

Returns:

Cramer’s V statistic

Example

>>> from torchmetrics.functional.nominal import cramers_v
>>> _ = torch.manual_seed(42)
>>> preds = torch.randint(0, 4, (100,))
>>> target = torch.round(preds + torch.randn(100)).clamp(0, 4)
>>> cramers_v(preds, target)
tensor(0.5284)


### cramers_v_matrix¶

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

Compute Cramer’s V statistic between a set of multiple variables.

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

Parameters:
Return type:

Tensor

Returns:

Cramer’s V statistic for a dataset of categorical variables

Example

>>> from torchmetrics.functional.nominal import cramers_v_matrix
>>> _ = torch.manual_seed(42)
>>> matrix = torch.randint(0, 4, (200, 5))
>>> cramers_v_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]])


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