DEPR: mad (mean absolute difference) functions

[aechase]

The generic function .mad() calculates the mean absolute difference of a set of data, but in some cases the median absolute difference is more appropriate. In R, the mad() function accepts a center argument to specify how the average absolute difference should be calculated. I propose to add the same to the pandas function.

[jreback]

we would do this as how='mean' as the default (and accept say median).

[shoyer]

df.mad() is equivalent to abs(df - df.mean()).mean(), which is much more explicit and obvious. Likewise, abs(df - df.median()).mean() would probably be better than df.mad(how='median') (note that from a performance perspective these are equivalent). I'm not entirely sure we really even need a separate .mad() method, though at this point I suppose there's little to gain from deprecating it.

[StephenKappel]

In R, the mad() function can never be used to calculate the mad() as currently defined in Pandas. The outer aggregator is always the median. Thecenter argument is a numeric constant and is used like this: abs(df - center).median().

Having an option to use the median in Pandas seems like a good idea; robustness is a common reason to use the MAD rather than standard deviation, but the current implementation is certainly not robust.

I think how should control the outer aggregator and adding a separate center argument similar to R's could be convenient and add clarity.

df.mad(how='median', center='median') would evaluate as abs(df - df.median()).median()

df.mad(how='median', center='mean') would evaluate as abs(df - df.mean()).median()

df.mad(how='median', center=15.4) would evaluate as abs(df - 15.4).median()

df.mad(how='mean', center='median') would evaluate as abs(df - df.median()).mean()

etc....

If this seems like a reasonable end-state, I can work on this issue.

[shoyer]

We could add a center keyword argument, but I would probably add documentation examples advising abs(x - x.median()).median() before adding both new keywords.

[BastiaanBergman]

• R implements MAD as:

constant * Median(abs(x - center))

where the constant is by default ~1.48 which makes it comparable to the standard deviation, the center is provided by the user (could be median or anything). R manual

• SAS implements MAD as:

median absolute deviation from the median

SAS manual

• JMP has a median absolute deviation, but doesn't abbreviate it. It has no mean absolute deviation.

Although there exists such a thing, there is not much use for a mean absolute deviation. Your data is either normally distributed and you use standard deviation and mean or it is not normally distributed and you cannot use this but might use median absolute deviation and median.

[shoyer]

Given all the potential confusion, I am almost inclined to deprecate this method instead. There are lots of ways to implement MAD, and it's almost better to force the user to implement their own rather than use the built-in one with mistaken assumptions.

Changing the implementation of methods like this is generally a non-starter because of a backwards compatibility concerns.

[andrewsanchez]

@shoyer @TomAugspurger I'm interested trying to implement this but wanted to check in first before getting to work, as the discussion was inconclusive. Does the recently added good first issue label mean this feature would be welcome? I think the improvement in code readability would be awesome.

[shoyer]

I'm not convinced that it make sense to iterate on this method. Given that we provide the primitives to implement this as a one-liner, I would recommend users write their own helper function for mad() and apply it with .pipe() if necessary.

[jreback]

i would be ok with deprecating .mad() entirely