Custom loss - correlation by column

1

Hi,

I’ve been having trouble computing my desired loss: I have two input tensors <X, Y>, with shapes: (batch_size, num_rows, num_columns). The loss I want to compute is the correlation between the respective <X, Y> columns for each one of the samples.

So far I’ve been iterating through each sample:

def cov(x, y):
    x_bar = x - x.mean(axis=0)
    y_bar = y - y.mean(axis=0)
    N = x_bar.shape[0]
    return (y_bar.T @ x_bar).T / (N - 1)


class Corr(nn.Module):
    def __init__(self, device, eps=1e-5):
        super(Corr, self).__init__()
        self.device = device
        self.eps = eps

    def forward(self, x, y, params):

        loss = 0
        for i in range(x.shape[0]):
            xi = x[i, :, :]
            yi = y[i, :, :]
            C_yy = cov(yi, yi)
            C_yx = cov(yi, xi)
            C_xx = cov(xi, xi)

            C_yy = C_yy + \
                torch.eye(C_yy.shape[0], device=self.device) * self.eps
            C_xx = C_xx + \
                torch.eye(C_xx.shape[0], device=self.device) * self.eps

            M = torch.linalg.multi_dot([torch.inverse(C_yy),
                                        C_yx,
                                        torch.inverse(C_xx),
                                        C_yx.T])

            loss += torch.trace(M)

        return (loss/x.shape[0])

Is there a faster way to implement this?

2

Hi Rane!

It’s relatively straightforward to implement a loop-free batch version of your
cov() function. Furthermore, torch.linalg.inv() (which torch.inverse()
is an alias for) computes matrix inverses on a batch basis if you pass in a
tensor with more than two dimensions. Together, these should give you the
tools to implement a loop-free version of your Corr loss.

Here is an illustration of a batch-cov() and batch-inv():

>>> import torch
>>> print (torch.__version__)
1.13.0
>>>
>>> _ = torch.manual_seed (2022)
>>>
>>> def cov(x, y):
...     x_bar = x - x.mean(axis=0)
...     y_bar = y - y.mean(axis=0)
...     N = x_bar.shape[0]
...     return (y_bar.T @ x_bar).T / (N - 1)
...
>>> def batchCov (x, y):
...     x_bar = x - x.mean (1).unsqueeze (1)
...     y_bar = y - y.mean (1).unsqueeze (1)
...     N = x_bar.shape[1]
...     return (y_bar.transpose (1, 2) @ x_bar).transpose (1, 2) / (N - 1)   # @ will do batch mm
...
>>> x = torch.randn (3, 5, 5)
>>> y = torch.randn (3, 5, 5)
>>>
>>> torch.allclose (batchCov (x, y)[2], cov (x[2], y[2]))
True
>>>
>>> torch.allclose (torch.linalg.inv (x)[2], torch.linalg.inv (x[2]))
True

Best.

K. Frank

1 Like
3

Thank you very much :smile: @KFrank,

I’ve used your batchCov function and modified my Corr to make it loop-free.