Kendallrankcorrcoef

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

# kendallrankcorrcoef

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

## When to invoke this skill

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

## Reference signature

```python
from torchmetrics import KendallRankCorrCoef

# KendallRankCorrCoef(variant: Literal['a', 'b', 'c'] = 'b', t_test: bool = False, alternative: Optional[Literal['two-sided', 'less', 'greater']] = 'two-sided', num_outputs: int = 1, **kwargs: Any) -> None
```

## Library docstring

```
Compute `Kendall Rank Correlation Coefficient`_.

.. math::
    tau_a = \frac{C - D}{C + D}

where :math:`C` represents concordant pairs, :math:`D` stands for discordant pairs.

.. math::
    tau_b = \frac{C - D}{\sqrt{(C + D + T_{preds}) * (C + D + T_{target})}}

where :math:`C` represents concordant pairs, :math:`D` stands for discordant pairs and :math:`T` represents
a total number of ties.

.. math::
    tau_c = 2 * \frac{C - D}{n^2 * \frac{m - 1}{m}}

where :math:`C` represents concordant pairs, :math:`D` stands for discordant pairs, :math:`n` is a total number
of observations and :math:`m` is a ``min`` of unique values in ``preds`` and ``target`` sequence.

Definitions according to Definition according to `The Treatment of Ties in Ranking Problems`_.

As input to ``forward`` and ``update`` the metric accepts the following input:

- ``preds`` (:class:`~torch.Tensor`): Sequence of data in float tensor of either shape ``(N,)`` or ``(N,d)``
- ``target`` (:class:`~torch.Tensor`): Sequence of data in float tensor of either shape ``(N,)`` or ``(N,d)``

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

- ``kendall`` (:class:`~torch.Tensor`): A tensor with the correlation tau statistic,
  and if it is not None, the p-value of corresponding statistical test.

Args:
    variant: Indication of which variant of Kendall's tau to be used
    t_test: Indication whether to run t-test
    alternative: Alternative hypothesis for t-test. Possible values:
        - 'two-sided': the rank correlation is nonzero
        - 'less': the rank correlation is negative (less than zero)
        - 'greater':  the rank correlation is positive (greater than zero)
    num_outputs: Number of outputs in multioutput setting
    kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.

Raises:
    ValueError: If ``t_test`` is not of a type bool
    ValueError: If ``t_test=True`` and ``alternative=None``

Example (single output regression):
    >>> from torch import tensor
    >>> from torchmetrics.regression import KendallRankCorrCoef
    >>> preds = tensor([2.5, 0.0, 2, 8])
    >>> target = tensor([3, -0.5, 2, 1])
    >>> kendall = KendallRa
```

## Quick recipe

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