Given an array of co-variance matrix; Convert each of them to correlation matrix in an efficient way without remove them from computation graph?

1

Consider I have an array of matrix M.shape = (N,D,D) where D is the dimension of co-variance matrix and N is the number of co-variance matrices.

I have a method that convert a single co-variance matrix to a correlation matrix defined as

def convert_to_correlation(m):
    inv = torch.inverse(torch.diag(torch.diag(m)).sqrt())
    r = inv@m@inv
    return r

When I have a list of such co-variance matrix I work as

def convert_all_to_correlation(M):
    res = []
    for i in range(len(M)):
        m = convert_to_correlation(M[i])
        res.append(m)
    res = torch.stack(res)
    return res

There are two problems in above approach;

(1) The array could have large first dimension; hence very slow in iterative loop
(2) My M is an output of neural network (hence part of computation graph); I don’t want my approach in convert_to_all_correlation remove them from graph.

Any help is appreciated! Thanks

2

Hi,

I’m a bit confused by your convert_to_correlation. It does not use m.

For 1: all the operations your use support batching (.diagonal, .inverse and matmul), so you can write a convert_to_correlation that works on the whole batch at once.
For 2: we have an implementation of derivatives for inversion and all other functions you use. So the result will be differentiable :slight_smile: (You can check that res.requires_grad = True).

3

Sorry; I got typo there; I’ve fixed the typo.

I’ve also checked the torch.diag() method; it seems only work on 2D tensor ?

4

Yes, .diag() is an old api that only supports 2D Tensor. That is why I mentionned .diagonal() above that is the new api that supports batching (and diag of arbitrary dimensions which is super cool).

5

Thanks for the advice. However, I’m confused with .diagonal() usage here

for example:

>>> x
 tensor([[[1,  2],
          [ 3, 4]],

          [[5, 6],
          [7,  8]]])

  >>> torch.diagona(x)

tensor([[1., 7.],
        [2., 8.]])

while I’m expecting with [[1,4],[5,8]]. Am I missing anything?

6

You can check the doc for the function.
If you want 1 4, 5 8, that means that you want the diagonal for the dimensions 1, 2 instead of the default 0, 1.

7

perfect ! Thanks for the help!