from typing import Optional, Sequence
import torch
import torch.nn as nn
from dalib.modules.classifier import Classifier as ClassifierBase
from dalib.modules.kernels import optimal_kernel_combinations
__all__ = ['MultipleKernelMaximumMeanDiscrepancy', 'ImageClassifier']
[docs]class MultipleKernelMaximumMeanDiscrepancy(nn.Module):
r"""The Multiple Kernel Maximum Mean Discrepancy (MK-MMD) used in
`Learning Transferable Features with Deep Adaptation Networks <https://arxiv.org/pdf/1502.02791>`_
Given source domain :math:`\mathcal{D}_s` of :math:`n_s` labeled points and target domain :math:`\mathcal{D}_t`
of :math:`n_t` unlabeled points drawn i.i.d. from P and Q respectively, the deep networks will generate
activations as :math:`\{z_i^s\}_{i=1}^{n_s}` and :math:`\{z_i^t\}_{i=1}^{n_t}`.
The MK-MMD :math:`D_k (P, Q)` between probability distributions P and Q is defined as
.. math::
D_k(P, Q) \triangleq \| E_p [\phi(z^s)] - E_q [\phi(z^t)] \|^2_{\mathcal{H}_k},
:math:`k` is a kernel function in the function space
.. math::
\mathcal{K} \triangleq \{ k=\sum_{u=1}^{m}\beta_{u} k_{u} \}
where :math:`k_{u}` is a single kernel.
Using kernel trick, MK-MMD can be computed as
.. math::
\hat{D}_k(P, Q) &=
\dfrac{1}{n_s^2} \sum_{i=1}^{n_s}\sum_{j=1}^{n_s} k(z_i^{s}, z_j^{s}) \\
&+ \dfrac{1}{n_t^2} \sum_{i=1}^{n_t}\sum_{j=1}^{n_t} k(z_i^{t}, z_j^{t}) \\
&- \dfrac{2}{n_s n_t} \sum_{i=1}^{n_s}\sum_{j=1}^{n_t} k(z_i^{s}, z_j^{t}). \\
Parameters:
- **kernels** (tuple(`nn.Module`)): kernel functions.
- **linear** (bool): whether use the linear version of DAN. Default: False
- **quadratic_program** (bool): whether use quadratic program to solve :math:`\beta`. Default: False
Inputs: z_s, z_t
- **z_s** (tensor): activations from the source domain, :math:`z^s`
- **z_t** (tensor): activations from the target domain, :math:`z^t`
Shape:
- Inputs: :math:`(minibatch, *)` where * means any dimension
- Outputs: scalar
.. note::
Activations :math:`z^{s}` and :math:`z^{t}` must have the same shape.
.. note::
The kernel values will add up when there are multiple kernels.
Examples::
>>> from dalib.modules.kernels import GaussianKernel
>>> feature_dim = 1024
>>> batch_size = 10
>>> kernels = (GaussianKernel(alpha=0.5), GaussianKernel(alpha=1.), GaussianKernel(alpha=2.))
>>> loss = MultipleKernelMaximumMeanDiscrepancy(kernels)
>>> # features from source domain and target domain
>>> z_s, z_t = torch.randn(batch_size, feature_dim), torch.randn(batch_size, feature_dim)
>>> output = loss(z_s, z_t)
"""
def __init__(self, kernels: Sequence[nn.Module], linear: Optional[bool] = False,
quadratic_program: Optional[bool] = False):
super(MultipleKernelMaximumMeanDiscrepancy, self).__init__()
self.kernels = kernels
self.index_matrix = None
self.linear = linear
self.quadratic_program = quadratic_program
def forward(self, z_s: torch.Tensor, z_t: torch.Tensor) -> torch.Tensor:
features = torch.cat([z_s, z_t], dim=0)
batch_size = int(z_s.size(0))
self.index_matrix = _update_index_matrix(batch_size, self.index_matrix, self.linear).to(z_s.device)
if not self.quadratic_program:
kernel_matrix = sum([kernel(features) for kernel in self.kernels]) # Add up the matrix of each kernel
# Add 2 / (n-1) to make up for the value on the diagonal
# to ensure loss is positive in the non-linear version
loss = (kernel_matrix * self.index_matrix).sum() + 2. / float(batch_size - 1)
else:
kernel_values = [(kernel(features) * self.index_matrix).sum() + 2. / float(batch_size - 1) for kernel in self.kernels]
loss = optimal_kernel_combinations(kernel_values)
return loss
def _update_index_matrix(batch_size: int, index_matrix: Optional[torch.Tensor] = None,
linear: Optional[bool] = True) -> torch.Tensor:
r"""
Update the `index_matrix` which convert `kernel_matrix` to loss.
If `index_matrix` is a tensor with shape (2 x batch_size, 2 x batch_size), then return `index_matrix`.
Else return a new tensor with shape (2 x batch_size, 2 x batch_size).
"""
if index_matrix is None or index_matrix.size(0) != batch_size * 2:
index_matrix = torch.zeros(2 * batch_size, 2 * batch_size)
if linear:
for i in range(batch_size):
s1, s2 = i, (i + 1) % batch_size
t1, t2 = s1 + batch_size, s2 + batch_size
index_matrix[s1, s2] = 1. / float(batch_size)
index_matrix[t1, t2] = 1. / float(batch_size)
index_matrix[s1, t2] = -1. / float(batch_size)
index_matrix[s2, t1] = -1. / float(batch_size)
else:
for i in range(batch_size):
for j in range(batch_size):
if i != j:
index_matrix[i][j] = 1. / float(batch_size * (batch_size - 1))
index_matrix[i + batch_size][j + batch_size] = 1. / float(batch_size * (batch_size - 1))
for i in range(batch_size):
for j in range(batch_size):
index_matrix[i][j + batch_size] = -1. / float(batch_size * batch_size)
index_matrix[i + batch_size][j] = -1. / float(batch_size * batch_size)
return index_matrix
class ImageClassifier(ClassifierBase):
def __init__(self, backbone: nn.Module, num_classes: int, bottleneck_dim: Optional[int] = 256):
bottleneck = nn.Sequential(
nn.Linear(backbone.out_features, bottleneck_dim),
nn.ReLU(),
nn.Dropout(0.5)
)
super(ImageClassifier, self).__init__(backbone, num_classes, bottleneck, bottleneck_dim, None)