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# Pearson’s Contingency Coefficient¶

## Module Interface¶

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

Compute Pearson’s Contingency Coefficient statistic.

This metric measures the association between two categorical (nominal) data series.

$Pearson = \sqrt{\frac{\chi^2 / n}{1 + \chi^2 / n}}$

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. Pearson’s Contingency Coefficient is a symmetric coefficient, i.e. $$Pearson(preds, target) = Pearson(target, preds)$$, 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:

• pearsons_cc (Tensor): Scalar tensor containing the Pearsons Contingency Coefficient statistic.

Parameters:
• num_classes (int) – Integer specifying the number of classes

• nan_strategy (Literal['replace', 'drop']) – Indication of whether to replace or drop NaN values

• nan_replace_value (Optional[float]) – Value to replace NaNs when nan_strategy = 'replace'

• kwargs (Any) – Additional keyword arguments, see Advanced metric settings for more info.

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 PearsonsContingencyCoefficient
>>> _ = torch.manual_seed(42)
>>> preds = torch.randint(0, 4, (100,))
>>> target = torch.round(preds + torch.randn(100)).clamp(0, 4)
>>> pearsons_contingency_coefficient = PearsonsContingencyCoefficient(num_classes=5)
>>> pearsons_contingency_coefficient(preds, target)
tensor(0.6948)
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:
Returns:

Figure and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

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

Compute Pearson’s Contingency Coefficient for measuring the association between two categorical data series.

$Pearson = \sqrt{\frac{\chi^2 / n}{1 + \chi^2 / n}}$

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.

Pearson’s Contingency Coefficient is a symmetric coefficient, i.e. $$Pearson(preds, target) = Pearson(target, preds)$$.

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)

• nan_strategy (Literal['replace', 'drop']) – Indication of whether to replace or drop NaN values

• nan_replace_value (Optional[float]) – Value to replace NaNs when nan_strategy = 'replace'

Return type:

Tensor

Returns:

Pearson’s Contingency Coefficient

Example

>>> from torchmetrics.functional.nominal import pearsons_contingency_coefficient
>>> _ = torch.manual_seed(42)
>>> preds = torch.randint(0, 4, (100,))
>>> target = torch.round(preds + torch.randn(100)).clamp(0, 4)
>>> pearsons_contingency_coefficient(preds, target)
tensor(0.6948)

### pearsons_contingency_coefficient_matrix¶

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

Compute Pearson’s Contingency Coefficient statistic between a set of multiple variables.

This can serve as a convenient tool to compute Pearson’s Contingency Coefficient 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 (Optional[float]) – Value to replace NaNs when nan_strategy = 'replace'

Return type:

Tensor

Returns:

Pearson’s Contingency Coefficient statistic for a dataset of categorical variables

Example

>>> from torchmetrics.functional.nominal import pearsons_contingency_coefficient_matrix
>>> _ = torch.manual_seed(42)
>>> matrix = torch.randint(0, 4, (200, 5))
>>> pearsons_contingency_coefficient_matrix(matrix)
tensor([[1.0000, 0.2326, 0.1959, 0.2262, 0.2989],
[0.2326, 1.0000, 0.1386, 0.1895, 0.1329],
[0.1959, 0.1386, 1.0000, 0.1840, 0.2335],
[0.2262, 0.1895, 0.1840, 1.0000, 0.2737],
[0.2989, 0.1329, 0.2335, 0.2737, 1.0000]])