def mmd_rbf_noaccelerate(source, target, kernel_mul=2.0, kernel_num=5, fix_sigma=None):
batch_size = int(source.size()[0])
kernels = guassian_kernel(source, target,
kernel_mul=kernel_mul, kernel_num=kernel_num, fix_sigma=fix_sigma)
XX = kernels[:batch_size, :batch_size]
YY = kernels[batch_size:, batch_size:]
XY = kernels[:batch_size, batch_size:]
YX = kernels[batch_size:, :batch_size]
loss = torch.mean(XX + YY - XY -YX)
return loss
def cmmd(source, target, s_label, t_label, kernel_mul=2.0, kernel_num=5, fix_sigma=None):
s_label = s_label.cpu()
s_label = s_label.view(32,1)
s_label = torch.zeros(32, 31).scatter_(1, s_label.data, 1)
s_label = Variable(s_label).cuda()
t_label = t_label.cpu()
t_label = t_label.view(32, 1)
t_label = torch.zeros(32, 31).scatter_(1, t_label.data, 1)
t_label = Variable(t_label).cuda()
batch_size = int(source.size()[0])
kernels = guassian_kernel(source, target,
kernel_mul=kernel_mul, kernel_num=kernel_num, fix_sigma=fix_sigma)
loss = 0
XX = kernels[:batch_size, :batch_size]
YY = kernels[batch_size:, batch_size:]
XY = kernels[:batch_size, batch_size:]
loss += torch.mean(torch.mm(s_label, torch.transpose(s_label, 0, 1)) * XX +
torch.mm(t_label, torch.transpose(t_label, 0, 1)) * YY -
2 * torch.mm(s_label, torch.transpose(t_label, 0, 1)) * XY)
return loss
import torch
def CORAL(source, target):
d = source.data.shape[1]
# source covariance
xm = torch.mean(source, 1, keepdim=True) - source
xc = torch.matmul(torch.transpose(xm, 0, 1), xm)
# target covariance
xmt = torch.mean(target, 1, keepdim=True) - target
xct = torch.matmul(torch.transpose(xmt, 0, 1), xmt)
# frobenius norm between source and target
loss = torch.mean(torch.mul((xc - xct), (xc - xct)))
loss = loss/(4*d*4)
return loss
import torch
import torch.nn as nn
# Adapted from https://github.com/gpeyre/SinkhornAutoDiff
class SinkhornDistance(nn.Module):
r"""
Given two empirical measures each with :math:`P_1` locations
:math:`x\in\mathbb{R}^{D_1}` and :math:`P_2` locations :math:`y\in\mathbb{R}^{D_2}`,
outputs an approximation of the regularized OT cost for point clouds.
Args:
eps (float): regularization coefficient
max_iter (int): maximum number of Sinkhorn iterations
reduction (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. Default: 'none'
Shape:
- Input: :math:`(N, P_1, D_1)`, :math:`(N, P_2, D_2)`
- Output: :math:`(N)` or :math:`()`, depending on `reduction`
"""
def __init__(self, eps, max_iter, reduction='none'):
super(SinkhornDistance, self).__init__()
self.eps = eps
self.max_iter = max_iter
self.reduction = reduction
def forward(self, x, y):
# The Sinkhorn algorithm takes as input three variables :
C = self._cost_matrix(x, y).cuda() # Wasserstein cost function
x_points = x.shape[-2]
y_points = y.shape[-2]
if x.dim() == 2:
batch_size = 1
else:
batch_size = x.shape[0]
# both marginals are fixed with equal weights
mu = torch.empty(batch_size, x_points, dtype=torch.float,
requires_grad=False).fill_(1.0 / x_points).squeeze().cuda()
nu = torch.empty(batch_size, y_points, dtype=torch.float,
requires_grad=False).fill_(1.0 / y_points).squeeze().cuda()
u = torch.zeros_like(mu)
v = torch.zeros_like(nu)
# To check if algorithm terminates because of threshold
# or max iterations reached
actual_nits = 0
# Stopping criterion
thresh = 1e-1
# Sinkhorn iterations
for i in range(self.max_iter):
u1 = u # useful to check the update
u = self.eps * (torch.log(mu+1e-8) - torch.logsumexp(self.M(C, u, v), dim=-1)) + u
v = self.eps * (torch.log(nu+1e-8) - torch.logsumexp(self.M(C, u, v).transpose(-2, -1), dim=-1)) + v
err = (u - u1).abs().sum(-1).mean()
actual_nits += 1
if err.item() < thresh:
break
U, V = u, v
# Transport plan pi = diag(a)*K*diag(b)
pi = torch.exp(self.M(C, U, V))
# Sinkhorn distance
cost = torch.sum(pi * C, dim=(-2, -1))
if self.reduction == 'mean':
cost = cost.mean()
elif self.reduction == 'sum':
cost = cost.sum()
return cost, pi, C
def M(self, C, u, v):
"Modified cost for logarithmic updates"
"$M_{ij} = (-c_{ij} + u_i + v_j) / \epsilon$"
return (-C + u.unsqueeze(-1) + v.unsqueeze(-2)) / self.eps
@staticmethod
def _cost_matrix(x, y, p=2):
"Returns the matrix of $|x_i-y_j|^p$."
x_col = x.unsqueeze(-2)
y_lin = y.unsqueeze(-3)
C = torch.sum((torch.abs(x_col - y_lin)) ** p, -1)
return C
@staticmethod
def ave(u, u1, tau):
"Barycenter subroutine, used by kinetic acceleration through extrapolation."
return tau * u + (1 - tau) * u1
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