Is Median Absolute Percentage Error useless? I'm working on a project focused on pricing houses.
Looking online I see a lot of works and companies providing the performances of their model using the median instead of the mean (see for example Zillow).
And to me this makes total sense, since its a statistic less influenced by outliers (in my scenario big and particular houses).
Also since I would like to have a greater interpretability of the performance of my model I used the Absolute Percentage Error, instead of the squared error.
In the end what I ended up using is the Median Absolute Percentage Error, and with my surprise I discovered that is not a common metrics, it doesn't have a wikipedia page, few sites provide an explanation of what it is, sklearn doesn't even have it as a metrics inside the sklearn.metrics._regression.py module.
And my question is: why?
Fixing it was a no brainer, really 2 line of code and I created my own version of it and I can easily run my model with this new metric, but I was wondering if maybe I'm missing something, like if its completely useless or maybe there are other metrics that works better.
If anyone could give me some insights that would be great!

I've spent a few years building real estate price regressors, which are known as "AVMs" (Automated Valuation Models).  A few comments:

*

*Yes, "median absolute percentage error" is both a reasonable metric and one that gets used in practice.  (And in an instance of catastrophic acronym failure, "MAPE" can refer either to "Mean" or "Median" absolute percent error.)

*Measuring "median absolute percentage error" is very strongly related to measuring "median absolute log error", and the latter has some advantages.

*

*If you're considering log error, then deviations become symmetric.  (This addresses quarague's observation about overestimating or underestimating by 2x.)

*Implementing this metric should be very easy-- you just take the log() of everything and evaluate the MAE().

*The logarithm also suppresses very large outliers (e.g., absurdly expensive mansions), which is one of the problems with examining real estate data. This can have both modeling and numerical stability advantages.  (There are also non-arms-length real estate deals, which lead to outliers that are very small, but these are frequently easier to detect.)



*There are companies that provide AVMs for banks and so forth; there are also companies that exist solely to evaluate the first set of companies.  If you're trying to understand standard evaluation methodology in this space, you may want to examine the latter.  To get started, maybe check out AVMetrics. (I have no connection with that company, by the way, aside from having read one of their analyses.)

