Pearsonscontingencycoefficient

---
name: pearsonscontingencycoefficient
description: Compute the PearsonsContingencyCoefficient metric — provided by torchmetrics. Use when the user has predictions and ground-truth and needs to compute PearsonsContingencyCoefficient, or asks how to score with PearsonsContingencyCoefficient.
metadata:
  skill_kind: metric
  source_lib: torchmetrics
  import_path: torchmetrics.PearsonsContingencyCoefficient
  source: library_introspection
---

# pearsonscontingencycoefficient

> Metric `PearsonsContingencyCoefficient` from `torchmetrics` (torchmetrics.PearsonsContingencyCoefficient)

## When to invoke this skill

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

## Reference signature

```python
from torchmetrics import PearsonsContingencyCoefficient

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

## Library docstring

```
Compute `Pearson's Contingency Coefficient`_ statistic.

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

.. math::
    Pearson = \sqrt{\frac{\chi^2 / n}{1 + \chi^2 / n}}

where

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

where :math:`n_{ij}` denotes the number of times the values :math:`(A_i, B_j)` are observed with :math:`A_i, B_j`
represent frequencies of values in ``preds`` and ``target``, respectively. Pearson's Contingency Coefficient is a
symmetric coefficient, i.e. :math:`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`` (:class:`~torch.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`` (:class:`~torch.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`` (:class:`~torch.Tensor`): Scalar tensor containing the Pearsons Contingency Coefficient 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.

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 torch import randint, randn
    >>> from torchmetrics.nominal import PearsonsContingencyCoefficient
    >>> preds = randint(0, 4, (100,))
    >>> target = (preds + randn(100)).round().clamp(0, 4)
    >>> pearsons_contingency
```

## Quick recipe

```python
import torchmetrics as _m
score = _m.PearsonsContingencyCoefficient(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)`.