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# MaximumMeanDiscrepancy#

class ignite.metrics.MaximumMeanDiscrepancy(var=1.0, output_transform=<function MaximumMeanDiscrepancy.<lambda>>, device=device(type='cpu'), skip_unrolling=False)[source]#

Calculates the mean of maximum mean discrepancy (MMD).

\begin{align*} \text{MMD}^2 (P,Q) &= \underset{\| f \| \leq 1}{\text{sup}} | \mathbb{E}_{X\sim P}[f(X)] - \mathbb{E}_{Y\sim Q}[f(Y)] |^2 \\ &\approx \frac{1}{B(B-1)} \sum_{i=1}^B \sum_{\substack{j=1 \\ j\neq i}}^B k(\mathbf{x}_i,\mathbf{x}_j) -\frac{2}{B^2}\sum_{i=1}^B \sum_{j=1}^B k(\mathbf{x}_i,\mathbf{y}_j) + \frac{1}{B(B-1)} \sum_{i=1}^B \sum_{\substack{j=1 \\ j\neq i}}^B k(\mathbf{y}_i,\mathbf{y}_j) \end{align*}

where $B$ is the batch size, and $\mathbf{x}_i$ and $\mathbf{y}_j$ are feature vectors sampled from $P$ and $Q$, respectively. $k(\mathbf{x},\mathbf{y})=\exp(-\| \mathbf{x}-\mathbf{y} \|^2/ 2\sigma^2)$ is the Gaussian RBF kernel.

This metric computes the MMD for each batch and takes the average.

More details can be found in Gretton et al. 2012.

• update must receive output of the form (x, y).

• x and y are expected to be in the same shape $(B, \ldots)$.

Parameters
• var (float) – the bandwidth $\sigma^2$ of the kernel. Default: 1.0

• 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, this metric requires the output as (x, y).

• device (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 (x, 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

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 = MaximumMeanDiscrepancy()
metric.attach(default_evaluator, "mmd")
x = torch.tensor([[-0.80324818, -0.95768364, -0.03807209],
[-0.11059691, -0.38230813, -0.4111988],
[-0.8864329, -0.02890403, -0.60119252],
[-0.68732452, -0.12854739, -0.72095073],
[-0.62604613, -0.52368328, -0.24112842]])
y = torch.tensor([[0.0686768, 0.80502737, 0.53321717],
[0.83849465, 0.59099726, 0.76385441],
[0.68688272, 0.56833803, 0.98100778],
[0.55267761, 0.13084654, 0.45382906],
[0.0754253, 0.70317304, 0.4756805]])
state = default_evaluator.run([[x, y]])
print(state.metrics["mmd"])

1.072697639465332


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. update Updates the metric's state using the passed batch output.
compute()[source]#

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()[source]#

Resets the metric to its initial state.

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

Return type

None

update(output)[source]#

Updates the metric’s state using the passed batch output.

By default, this is called once for each batch.

Parameters

output (Sequence[Tensor]) – the is the output from the engine’s process function.

Return type

None

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