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kl_divergence.py
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kl_divergence.py
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# Copyright The PyTorch Lightning team.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Optional, Tuple
import torch
from torch import Tensor
from torchmetrics.utilities.checks import _check_same_shape
from torchmetrics.utilities.data import METRIC_EPS
def _kld_update(p: Tensor, q: Tensor, log_prob: bool) -> Tuple[Tensor, int]:
_check_same_shape(p, q)
if p.ndim != 2 or q.ndim != 2:
raise ValueError(f"Expected both p and q distribution to be 2D but got {p.ndim} and {q.ndim} respectively")
total = p.shape[0]
if log_prob:
measures = torch.sum(p.exp() * (p - q), axis=-1)
else:
p = p / p.sum(axis=-1, keepdim=True)
q = q / q.sum(axis=-1, keepdim=True)
q = torch.clamp(q, METRIC_EPS)
measures = torch.sum(p * torch.log(p / q), axis=-1)
return measures, total
def _kld_compute(measures: Tensor, total: Tensor, reduction: Optional[str] = 'mean') -> Tensor:
if reduction == 'sum':
return measures.sum()
if reduction == 'mean':
return measures.sum() / total
if reduction is None or reduction == 'none':
return measures
return measures / total
def kldivergence(p: Tensor, q: Tensor, log_prob: bool = False, reduction: Optional[str] = 'mean') -> Tensor:
r"""Computes the `KL divergence <https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence>`_:
.. math::
D_{KL}(P||Q) = \sum_{x\in\mathcal{X}} P(x) \log\frac{P(x)}{Q{x}}
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`. It should be noted that the KL divergence
is a non-symetrical metric i.e. :math:`D_{KL}(P||Q) \neq D_{KL}(Q||P)`.
Args:
p: data distribution with shape ``[N, d]``
q: prior or approximate distribution with shape ``[N, d]``
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
Example:
>>> import torch
>>> from torchmetrics.functional import kldivergence
>>> p = torch.tensor([[0.36, 0.48, 0.16]])
>>> q = torch.tensor([[1/3, 1/3, 1/3]])
>>> kldivergence(p, q)
tensor(0.0853)
"""
measures, total = _kld_update(p, q, log_prob)
return _kld_compute(measures, total, reduction)