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kl_divergence.py
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kl_divergence.py
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# Copyright The 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 Any, Optional, Sequence, Union
import torch
from torch import Tensor
from typing_extensions import Literal
from torchmetrics.functional.regression.kl_divergence import _kld_compute, _kld_update
from torchmetrics.metric import Metric
from torchmetrics.utilities.data import dim_zero_cat
from torchmetrics.utilities.imports import _MATPLOTLIB_AVAILABLE
from torchmetrics.utilities.plot import _AX_TYPE, _PLOT_OUT_TYPE
if not _MATPLOTLIB_AVAILABLE:
__doctest_skip__ = ["KLDivergence.plot"]
class KLDivergence(Metric):
r"""Compute the `KL 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-symmetrical metric i.e. :math:`D_{KL}(P||Q) \neq D_{KL}(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:
- ``kl_divergence`` (:class:`~torch.Tensor`): A tensor with the KL 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``.
.. 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)
"""
is_differentiable: bool = True
higher_is_better: bool = False
full_state_update: bool = False
plot_lower_bound: float = 0.0
total: Tensor
# FIXME: Apply once minimal torch is 1.10. For torch<=1.9, jit does not support Union types
# measures: Union[Tensor, List[Tensor]]
def __init__(
self,
log_prob: bool = False,
reduction: Literal["mean", "sum", "none", None] = "mean",
**kwargs: Any,
) -> None:
super().__init__(**kwargs)
if not isinstance(log_prob, bool):
raise TypeError(f"Expected argument `log_prob` to be bool but got {log_prob}")
self.log_prob = log_prob
allowed_reduction = ["mean", "sum", "none", None]
if reduction not in allowed_reduction:
raise ValueError(f"Expected argument `reduction` to be one of {allowed_reduction} but got {reduction}")
self.reduction = reduction
if self.reduction in ["mean", "sum"]:
self.add_state("measures", torch.tensor(0.0), dist_reduce_fx="sum")
else:
self.add_state("measures", [], dist_reduce_fx="cat")
self.add_state("total", torch.tensor(0), dist_reduce_fx="sum")
def update(self, p: Tensor, q: Tensor) -> None:
"""Update metric states with predictions and targets."""
measures, total = _kld_update(p, q, self.log_prob)
if self.reduction is None or self.reduction == "none":
self.measures.append(measures)
else:
self.measures += measures.sum()
self.total += total
def compute(self) -> Tensor:
"""Compute metric."""
measures: Tensor = dim_zero_cat(self.measures) if self.reduction in ["none", None] else self.measures
return _kld_compute(measures, self.total, self.reduction)
def plot(
self, val: Optional[Union[Tensor, Sequence[Tensor]]] = None, ax: Optional[_AX_TYPE] = None
) -> _PLOT_OUT_TYPE:
"""Plot a single or multiple values from the metric.
Args:
val: 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: An matplotlib axis object. If provided will add plot to that axis
Returns:
Figure and Axes object
Raises:
ModuleNotFoundError:
If `matplotlib` is not installed
.. plot::
:scale: 75
>>> 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()
.. plot::
:scale: 75
>>> 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)
"""
return self._plot(val, ax)