基于统计对齐的域适应方法（MMD,CMMD,CORAL,Wasserstein distance ）

一：Maximum mean discrepancy (MMD)

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

二：Conditional maximum mean discrepancy (CMMD)

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

三：CORAL

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

四：Wasserstein distance

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