Inconsistent error definition

[codingWhale13]

Currently, the meaning of error doesn't seem consistent. Concretely, MSE uses target - forecast.mean as error while other metrics (absolute error, MAPE, ...) define the error as target - forecast.median.

Is this a conscious decision or would it make sense to stick to one definition?

For context, see here.

[lostella]

It's a conscious decision. Under the assumption that the predicted distribution (forecast) is what target is sampled from, then:

• the mean of the distribution minimizes the mean squared error
• the median of the distribution minimizes the mean absolute error

[jaheba]

Maybe something we can do is to document this better. So for each metric using mean or median we could highlight which one is used and why.