Jensenshannondivergence

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

# jensenshannondivergence

> Metric `JensenShannonDivergence` from `torchmetrics` (torchmetrics.regression.JensenShannonDivergence)

## When to invoke this skill

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

## Reference signature

```python
from torchmetrics.regression import JensenShannonDivergence

# JensenShannonDivergence(log_prob: bool = False, reduction: Literal['mean', 'sum', 'none', None] = 'mean', **kwargs: Any) -> None
```

## Library docstring

```
Compute the `Jensen-Shannon divergence`_.

.. math::
    D_{JS}(P||Q) = \frac{1}{2} D_{KL}(P||M) + \frac{1}{2} D_{KL}(Q||M)

Where :math:`P` and :math:`Q` are probability distributions where :math:`P` usually represents a distribution
over data and :math:`Q` is often a prior or approximation of :math:`P`. :math:`D_{KL}` is the `KL divergence`_ and
:math:`M` is the average of the two distributions. It should be noted that the Jensen-Shannon divergence is a
symmetrical metric i.e. :math:`D_{JS}(P||Q) = D_{JS}(Q||P)`.

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

- ``p`` (:class:`~torch.Tensor`): a data distribution with shape ``(N, d)``
- ``q`` (:class:`~torch.Tensor`): prior or approximate distribution with shape ``(N, d)``

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

- ``js_divergence`` (:class:`~torch.Tensor`): A tensor with the Jensen-Shannon divergence

Args:
    log_prob: bool indicating if input is log-probabilities or probabilities. If given as probabilities,
        will normalize to make sure the distributes sum to 1.
    reduction:
        Determines how to reduce over the ``N``/batch dimension:

        - ``'mean'`` [default]: Averages score across samples
        - ``'sum'``: Sum score across samples
        - ``'none'`` or ``None``: Returns score per sample

    kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.

Raises:
    TypeError:
        If ``log_prob`` is not an ``bool``.
    ValueError:
        If ``reduction`` is not one of ``'mean'``, ``'sum'``, ``'none'`` or ``None``.

.. attention::
    Half precision is only support on GPU for this metric.

Example:
    >>> from torch import tensor
    >>> from torchmetrics.regression import JensenShannonDivergence
    >>> p = tensor([[0.1, 0.9], [0.2, 0.8], [0.3, 0.7]])
    >>> q = tensor([[0.3, 0.7], [0.4, 0.6], [0.5, 0.5]])
    >>> js_div = JensenShannonDivergence()
    >>> js_div(p, q)
    tensor(0.0259)
```

## Quick recipe

```python
import torchmetrics.regression as _m
score = _m.JensenShannonDivergence(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)`.