KL Divergence

Module Interface

class torchmetrics.KLDivergence(log_prob=False, reduction='mean', **kwargs)

Compute the KL divergence.

\[D_{KL}(P||Q) = \sum_{x\in\mathcal{X}} P(x) \log\frac{P(x)}{Q{x}}\]

Where \(P\) and \(Q\) are probability distributions where \(P\) usually represents a distribution over data and \(Q\) is often a prior or approximation of \(P\). It should be noted that the KL divergence is a non-symmetrical metric i.e. \(D_{KL}(P||Q) \neq D_{KL}(Q||P)\).

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

• p (Tensor): a data distribution with shape (N, d)

• q (Tensor): prior or approximate distribution with shape (N, d)

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

• kl_divergence (Tensor): A tensor with the KL divergence

Parameters:

• log_prob (bool) – bool indicating if input is log-probabilities or probabilities. If given as probabilities, will normalize to make sure the distributes sum to 1.

• reduction (Literal['mean', 'sum', 'none', None]) –

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

Raises:

• TypeError – If log_prob is not an bool.

• ValueError – If reduction is not one of 'mean', 'sum', 'none' or None.

Note

Half precision is only support on GPU for this metric

Example

>>> from torch import tensor
>>> from torchmetrics.regression import KLDivergence
>>> p = tensor([[0.36, 0.48, 0.16]])
>>> q = tensor([[1/3, 1/3, 1/3]])
>>> kl_divergence = KLDivergence()
>>> kl_divergence(p, q)
tensor(0.0853)

plot(val=None, ax=None)

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:

Tuple[Figure, Union[Axes, ndarray]]

Returns:

Figure and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

>>> from torch import randn
>>> # Example plotting a single value
>>> from torchmetrics.regression import KLDivergence
>>> metric = KLDivergence()
>>> metric.update(randn(10,3).softmax(dim=-1), randn(10,3).softmax(dim=-1))
>>> fig_, ax_ = metric.plot()

>>> from torch import randn
>>> # Example plotting multiple values
>>> from torchmetrics.regression import KLDivergence
>>> metric = KLDivergence()
>>> values = []
>>> for _ in range(10):
...     values.append(metric(randn(10,3).softmax(dim=-1), randn(10,3).softmax(dim=-1)))
>>> fig, ax = metric.plot(values)

Functional Interface

torchmetrics.functional.kl_divergence(p, q, log_prob=False, reduction='mean')

Compute KL divergence.

\[D_{KL}(P||Q) = \sum_{x\in\mathcal{X}} P(x) \log\frac{P(x)}{Q{x}}\]

Where \(P\) and \(Q\) are probability distributions where \(P\) usually represents a distribution over data and \(Q\) is often a prior or approximation of \(P\). It should be noted that the KL divergence is a non-symmetrical metric i.e. \(D_{KL}(P||Q) \neq D_{KL}(Q||P)\).

Parameters:

• p (Tensor) – data distribution with shape [N, d]

• q (Tensor) – prior or approximate distribution with shape [N, d]

• log_prob (bool) – bool indicating if input is log-probabilities or probabilities. If given as probabilities, will normalize to make sure the distributes sum to 1

• reduction (Literal['mean', 'sum', 'none', None]) –

  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

Return type:

Tensor

Example

>>> from torch import tensor
>>> p = tensor([[0.36, 0.48, 0.16]])
>>> q = tensor([[1/3, 1/3, 1/3]])
>>> kl_divergence(p, q)
tensor(0.0853)