Hi,
I am trying to implement an energy score loss for a forecast ensemble.

energy-score944×176 6.34 KB

I’m having trouble vectorizing the second term, which is essentially a sum over pairwise distances between different ensemble members (i != j) of the forecast tensor X. X.shape = (batch_size, n_vars, lat, lon, n_members) and the (i, j) index the n_members dimension (X.shape[-1]).
Here’s the “loopy” version i coded for a single sample:
    # works only with a batch_size == 1
    tmp_b = torch.zeros(1)
    for i in range(m):
        for j in range(m):
            if i == j:
                continue
            # i am using a more general formula where each 2-norm is raised to the power beta
            tmp_b += torch.pow(torch.linalg.norm((y_pred[..., i] - y_pred[..., j]).flatten(), ord=2), beta)

    # unbiased estimator: divide by (m-1) instead of m as the i = j terms cancel out
    tmp_b *= - 1.0 / (2 * m * (m - 1))

So I have two questions:
1/ How to vectorize the code above?
2/ How to vectorize the formula for batch_size > 1 (essentially this would entail averaging over the energy losses for all samples in the batch)
Thanks!