Change of the multiplication order for covariance calculation

[abhijeetdhakane]

Hello,

I have a question about, the following code from:

https://github.com/deeptime-ml/deeptime/blob/8dc85b3e40e6b16f78212ac9aa412532ff138ce1/deeptime/decomposition/deep/_vampnet.py

# Calculate the cross-covariance
y_t = y.transpose(0, 1)
x_t = x.transpose(0, 1)

cov_01 = 1 / (batch_size - 1) * torch.matmul(x_t, y)
# Calculate the auto-correlations
cov_00 = 1 / (batch_size - 1) * torch.matmul(x_t, x)
cov_11 = 1 / (batch_size - 1) * torch.matmul(y_t, y)

What if I change it into

# Calculate the cross-covariance

y_t = y.transpose(0, 1)
x_t = x.transpose(0, 1)
cov_01 = 1 / (batch_size - 1) * torch.matmul(x, y_t)
# Calculate the auto-correlations
cov_00 = 1 / (batch_size - 1) * torch.matmul(x, x_t)
cov_11 = 1 / (batch_size - 1) * torch.matmul(y, y_t)`

Does this still work? (Well it will work, but is it right?)

[clonker]

Hey, if we think about x \in R^{T, n_features}, then cov_00 describes the covariances between features. Your change modifies this meaning entirely, I do not think it is right in this context. 🙂

[abhijeetdhakane]

You're right!