Hello,

I was reading the cross-entropy definition from the Lokad website, and I am having trouble understanding how to use cross-entropy loss in demand forecasting.

https://www.lokad.com/cross-entropy-definition/

I am familiar with cross entropy loss in classification problems, where

$\text{Loss} = -\sum_{i=1}^{n} y_i * \log \hat{y}_{i}$

and $n$ is the number of classes we have. In this case, $y_i$ would always be either 0 or 1, and $\hat{y}_{i}$ is the softmax probability for i-th class. Usually, we can get the average Cross Entropy Loss across all data points, and adjust our weights to minimize that loss with gradient descent.

But how do we formulate this in a forecasting problem? Would our classes be all discrete numbers in $[0,\infty]$, and our $y_i$'s 0, except for the actual demand value, which would be 1?

In the article, it is mentioned that Lokad collected empirical data which supports the claim that Cross Entropy is usually the most efficient metric to optimize, rather than MSE, MAPE, CRPS, etc. Is it possible to view that data?

Thanks,
Tom Murray