MutualInformation

class ignite.metrics.MutualInformation(output_transform=<function Metric.<lambda>>, device=device(type='cpu'), skip_unrolling=False)

Calculates the mutual information between input $X$ and prediction $Y$.

$$\begin{align*} I(X;Y) &= H(Y) - H(Y|X) = H \left( \frac{1}{N}\sum_{i=1}^N \hat{\mathbf{p}}_i \right) - \frac{1}{N}\sum_{i=1}^N H(\hat{\mathbf{p}}_i), \\ H(\mathbf{p}) &= -\sum_{c=1}^C p_c \log p_c. \end{align*}$$

where $\hat{\mathbf{p}}_i$ is the prediction probability vector for $i$-th input, and $H(\mathbf{p})$ is the entropy of $\mathbf{p}$.

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. $(B, C)$ (classification) or $(B, C, ...)$ (e.g., image segmentation) shapes are allowed.

Parameters

• output_transform (Callable) – a callable that is used to transform the 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 (Union[str, 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 (bool) – 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 Engine, visit Attach Engine API.

from collections import OrderedDict

import torch
from torch import nn, optim

from ignite.engine import *
from ignite.handlers import *
from ignite.metrics import *
from ignite.metrics.regression import *
from ignite.utils import *

# create default evaluator for doctests

def eval_step(engine, batch):
    return batch

default_evaluator = Engine(eval_step)

# create default optimizer for doctests

param_tensor = torch.zeros([1], requires_grad=True)
default_optimizer = torch.optim.SGD([param_tensor], lr=0.1)

# create default trainer for doctests
# as handlers could be attached to the trainer,
# each test must define his own trainer using `.. testsetup:`

def get_default_trainer():

    def train_step(engine, batch):
        return batch

    return Engine(train_step)

# create default model for doctests

default_model = nn.Sequential(OrderedDict([
    ('base', nn.Linear(4, 2)),
    ('fc', nn.Linear(2, 1))
]))

manual_seed(666)

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'])

0.18599730730056763

Changed in version 0.5.1: skip_unrolling argument is added.

Methods

compute	Computes the metric based on its accumulated state.
reset	Resets the metric to its initial state.

compute()

Computes the metric based on its accumulated state.

By default, this is called at the end of each epoch.

Returns

the actual quantity of interest. However, if a Mapping is returned, it will be (shallow) flattened into engine.state.metrics when completed() is called.

Return type

Any

Raises

NotComputableError – raised when the metric cannot be computed.

reset()

Resets the metric to its initial state.

By default, this is called at the start of each epoch.

Return type

None