Talk:Mean absolute percentage error

The formula is not the same as what I learned in my business class right now. ~Fulano (visitor)

What formula did you learn, and do you have a source? Paul2520 (talk) 15:02, 19 September 2013 (UTC)

Do not merge other error metrics with this article

Please do not merge WMAPE or any other article into this! WMAPE is not an "alternative definition of MAPE" as some of the unfortunate edits suggest. Wikipedia has separate articles for different metrics: Mean Absolute Scaled Error (MASE), Symmetric Mean Absolute Percentage Error (sMAPE), Mean Directional Accuracy (MDA) etc. and should continue to have so. — Preceding unsigned comment added by Manu.m (talk • contribs) 07:45, 30 June 2022 (UTC)

Percentage & multiplication by 100

In the current form, the formula is

${\mbox{MAPE}}={\frac {100}{n}}\sum _{t=1}^{n}\left|{\frac {A_{t}-F_{t}}{A_{t}}}\right|$

The article then says "The MAPE is also sometimes reported as a percentage, which is the above equation multiplied by 100". Isn't the formula already multiplied by 100?91.68.56.209 (talk) 07:16, 16 June 2021 (UTC)

Reorganize the article

This article should be restructured because

- issues related to the MAPE are listed both in introduction and in the section "issues"

- it lacks a section on MAPE regressions, since this is also very popular metric in Machine Learning (like Mean squared error)

(unsigned, posted by Adm4749d) North8000 (talk) 23:33, 13 December 2018 (UTC)

Source

A good source for the formula is the following article: https://www.sciencedirect.com/science/article/pii/S0169207016000121

--PoulsHaut (talk) 13:05, 9 December 2021 (UTC)

Proposed merger

I propose merging WMAPE into Mean absolute percentage error. Weighted MAPE is merely a variation of MAPE. Having two separate articles is potentially redundant and results in significant overlap. Merger is recommended per WP:OVERLAP.

I performed the merger on June 4. See edits to WMAPE and MAPE. The merger was reverted on June 30, so I am now seeking consensus on whether to merge.

@Manu.m -- I appreciate your input. Thanks! Edge3 (talk) 02:52, 8 July 2022 (UTC)

• Support. As Manu.m pointed out in the edit summary, "Alternative definitions" is the wrong header name to use. But there is too much similarity between the topics to have separate articles. The content at WMAPE should be placed into a top-level section called "Weighted mean absolute percentage error". Wikiacc (¶) 02:51, 12 July 2022 (UTC)

  Y Merger complete. Klbrain (talk) 07:37, 16 November 2022 (UTC)

Issues of MAPE

I don't understand the part that claims that (M)APE gives a different bias to positive and negative values. Suppose, the true value is $A_t=100$. If $F_t=150$, deviating by +50 in absolute values, I get MAPE=50 %. If instead $F_t=50$, deviating by -50, I similarly get MAPE=50%. In both cases the same relative absolute error is made. And if I plot MAPE versus the deviation (A_t-F_t) I get a totally symmetric curve (just two linear parts of abs). So, where is the problem?

It seems, that Makridakis et. al. assume that the roles of $A_t$ and $F_t$ are interchanged. But this uses a different baseline for the two cases. The MAPE always is relative on the true value, this is its precondition. And if I change the true value, I cannot compare, i.e. I cannot compare MAPEs with the same deviation between true and predicted values on an absolute scale if the true values are different. In the example of Makridakis et. al we have |(100-150)/100|=50% for A_t=100 but |(150-100)/150|=33% for A_t=150. But this is IMHO not a demonstration of assymmetry because we change the baseline. The relative error is different because the size of A_t is different. But for the both cases, if I made the same delta to the other direction the MAPEs would be totally the same: |(100-50)/100|=50% and |(150-200)/150|=33%. MAPE is totally symmetric in the difference between true and predicted value on a absolute scale and this symmetry is with respect to the ture value. $|(A_t-(A_t+\Delta))/A_t|=|(A_t-(A_t-\Delta))/A_t$!!

I rather would mention the problem that MAPE is not invariant to a shift of the scale or a shift of A_t:

$|(A_t-(A_t+\Delta))/A_t|=|(A_t+C-(A_t+C-\Delta))/(A_t+C)$.

Example:

|(100-150)/100|=50% but |(1000-1050)/1000|=5% (shifted by 900)

I also don't understand the claim the MAPE has a lower bound of 100 % for negative errors. Suppose, $A_t=100$, then

|(100-(-100))/100|=200% for $F_t=-200$.

This bound is only valid if $F_t$ cannot have negative values. Otherwise, MAPE is unbound in both directions of a deviation. HoockB (talk) 11:36, 8 October 2024 (UTC)