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import torch
from ignite.exceptions import NotComputableError
from ignite.metrics import Entropy
from ignite.metrics.metric import reinit__is_reduced, sync_all_reduce
__all__ = ["MutualInformation"]
class MutualInformation(Entropy):
r"""Calculates the `mutual information <https://en.wikipedia.org/wiki/Mutual_information>`_
between input :math:`X` and prediction :math:`Y`.
.. math::
\begin{align*}
I(X;Y) &= H(Y) - H(Y|X) = H \left( \frac{1}{N}\sum_{i=1}^N \hat{\mathbf{p}}_i \right)
- \frac{1}{N}\sum_{i=1}^N H(\hat{\mathbf{p}}_i), \\
H(\mathbf{p}) &= -\sum_{c=1}^C p_c \log p_c.
\end{align*}
where :math:`\hat{\mathbf{p}}_i` is the prediction probability vector for :math:`i`-th input,
and :math:`H(\mathbf{p})` is the entropy of :math:`\mathbf{p}`.
Intuitively, this metric measures how well input data are clustered by classes in the feature space [1].
[1] https://proceedings.mlr.press/v70/hu17b.html
- ``update`` must receive output of the form ``(y_pred, y)`` while ``y`` is not used in this metric.
- ``y_pred`` is expected to be the unnormalized logits for each class. :math:`(B, C)` (classification)
or :math:`(B, C, ...)` (e.g., image segmentation) shapes are allowed.
Args:
output_transform: a callable that is used to transform the
:class:`~ignite.engine.engine.Engine`'s ``process_function``'s output into the
form expected by the metric. This can be useful if, for example, you have a multi-output model and
you want to compute the metric with respect to one of the outputs.
By default, metrics require the output as ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y}``.
device: specifies which device updates are accumulated on. Setting the
metric's device to be the same as your ``update`` arguments ensures the ``update`` method is
non-blocking. By default, CPU.
skip_unrolling: specifies whether output should be unrolled before being fed to update method. Should be
true for multi-output model, for example, if ``y_pred`` contains multi-ouput as ``(y_pred_a, y_pred_b)``
Alternatively, ``output_transform`` can be used to handle this.
Examples:
To use with ``Engine`` and ``process_function``, simply attach the metric instance to the engine.
The output of the engine's ``process_function`` needs to be in the format of
``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y, ...}``. If not, ``output_tranform`` can be added
to the metric to transform the output into the form expected by the metric.
For more information on how metric works with :class:`~ignite.engine.engine.Engine`, visit :ref:`attach-engine`.
.. include:: defaults.rst
:start-after: :orphan:
.. testcode::
metric = MutualInformation()
metric.attach(default_evaluator, 'mutual_information')
y_true = torch.tensor([0, 1, 2]) # not considered in the MutualInformation metric.
y_pred = torch.tensor([
[ 0.0000, 0.6931, 1.0986],
[ 1.3863, 1.6094, 1.6094],
[ 0.0000, -2.3026, -2.3026]
])
state = default_evaluator.run([[y_pred, y_true]])
print(state.metrics['mutual_information'])
.. testoutput::
0.18599730730056763
.. versionchanged:: 0.5.1
``skip_unrolling`` argument is added.
"""
_state_dict_all_req_keys = ("_sum_of_probabilities",)
@reinit__is_reduced
def reset(self) -> None:
super().reset()
self._sum_of_probabilities = torch.tensor(0.0, device=self._device)
def _update(self, prob: torch.Tensor, log_prob: torch.Tensor) -> None:
super()._update(prob, log_prob)
# We can't use += below as _sum_of_probabilities can be a scalar and prob.sum(dim=0) is a vector
self._sum_of_probabilities = self._sum_of_probabilities + prob.sum(dim=0).to(self._device)
@sync_all_reduce("_sum_of_probabilities", "_sum_of_entropies", "_num_examples")
def compute(self) -> float:
n = self._num_examples
if n == 0:
raise NotComputableError("MutualInformation must have at least one example before it can be computed.")
marginal_prob = self._sum_of_probabilities / n
marginal_ent = -(marginal_prob * torch.log(marginal_prob)).sum()
conditional_ent = self._sum_of_entropies / n
mi = marginal_ent - conditional_ent
mi = torch.clamp(mi, min=0.0) # mutual information cannot be negative
return float(mi.item())
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