I am trying to understand sklearn's new MAPE function. It is mentioned in the documentation that
we do not represent the output as a percentage in range [0, 100]. Instead, we represent it in range [0, 1/eps]. Read more in the User Guide.
What is eps? And how can I possibly convert the values obtained from this MAPE to percentage?
The User Guide link that you already know about explains that "ε is an arbitrary small yet strictly positive number to avoid undefined results when y is zero", but it doesn't state what that value actually is.
You can find the definition in the code to be:
epsilon = np.finfo(np.float64).eps
which is the smallest positive 64 bit floating point number such that 1 + eps ≠ 1. The value is 2⁻⁵² ≈ 2.22e-16. (See the documentation for numpy.finfo for more information.)
To convert to a percentage, just multiply the return value of mean_absolute_percentage_error by 100.
Note: The comment "we do not represent the output as a percentage in range [0, 100]" is potentially misleading. When expressed as a percentage by multiplying by 100, the MAPE will not necessarily be in the range [0, 100]. For example, if the data is, say, y_true = [1, 1, 1] and y_pred = [1, 4, 2.5], the MAPE computed by
mean_absolute_percentage_error(y_true, y_pred)
is 1.5, which expressed as a percentage is 150%. I think the intent of the comment is to make clear that--despite what the name might imply--they don't multiply by 100, so the result is a fraction, not a percentage. That fraction can certainly be greater than 1, and so the percentage can be greater than 100.
