How to find the mean and the covariance of a 2d activation map (pytorch)

0
votes

I have a tensor of shape [h, w], which consists of a normalized, 2-dimensional activation map. Considering this to be some distribution, I want to find the mean and the covariance within this activation map in pytorch. Is there an efficient way to do that?

2
pytorchmeandistributioncovariance
Do you want to compute the mean and covariance along a particular dimension, or for the tensor as a whole? – Ben
@ Ben for that tensor as a whole, so the covariance should be a 2x2 matrix as far as I understand. – spadel
stackoverflow.com/questions/51416825/… for two channels – prosti

2 Answers

2
votes

You can use the following code, where activation_map is a tensor of shape (h,w), with non-negative elements, and is normalised (activation_map.sum() is 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, 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]])
0
votes

One way for the covariance matrix:

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)

Out:

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,  0.6787,  0.9545,  0.9972, -0.8001],
        [-0.1197,  1.1938,  0.9972,  2.0169, -1.3110],
        [ 0.3957, -1.5568, -0.8001, -1.3110,  1.4546]])

The mean() should be trivial just refer the documentation.