如何找到二维激活图pytorch的均值和协方差

问题描述

我有一个张量为[h，w]的张量，它由归一化的二维激活图组成。考虑到这是某种分布，我想在pytorch中找到此激活图中的均值和协方差。有有效的方法吗？

解决方法

您可以使用以下代码，其中activation_map是形状为(h,w)的张量，具有非负元素，并且已规范化（activation_map.sum()为1）：

activation_map = torch.tensor(
    [[0.2,0.1,0.0],[0.1,0.2,0.4]])
h,w = activation_map.shape

range_h = torch.arange(h)
range_w = torch.arange(w)
idxs = torch.stack([
  range_w[None].repeat(h,1),range_h[:,None].repeat(1,w)
  ])
map_flat = activation_map.view(-1)
idxs_flat = idxs.reshape(2,-1).T
mean = (map_flat[:,None] * idxs_flat).sum(0)
mats = idxs_flat[:,:,None] @ idxs_flat[:,None,:]
second_moments = (map_flat[:,None] * mats).sum(0)
covariance = second_moments - mean[:,None] @ mean[None]

# mean:
# tensor([1.1000,0.7000])
# covariance:
# tensor([[0.6900,0.2300],#         [0.2300,0.2100]])

,

协方差矩阵的一种方法：

h,w = 3,5

def cov(X):
    X = X/np.sqrt(X.size(0) - 1)
    return X.T @ X

x = torch.randn(h,w)
print(x)

c = cov(x)
print(c)

出局：

tensor([[-1.5029e-01,-2.0626e-01,-7.7845e-01,-1.6811e+00,5.0312e-01],[ 4.4658e-01,-1.8570e+00,-6.2250e-01,-1.0989e+00,1.6159e+00],[ 6.8612e-01,-4.2650e-02,-9.5685e-01,-1.7947e-03,2.1187e-01]])
tensor([[ 0.3464,-0.4138,-0.4088,-0.1197,0.3957],[-0.4138,1.7464,0.6787,1.1938,-1.5568],[-0.4088,0.9545,0.9972,-0.8001],[-0.1197,2.0169,-1.3110],[ 0.3957,-1.5568,-0.8001,-1.3110,1.4546]])

mean()应该是trivial，只需参考文档即可。