
Median and Mad Revisited with an Online Estimator - AnthonyLloyd
http://anthonylloyd.github.io/blog/2020/04/07/Median-Revisited
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asplake
MAD being mean absolute deviation
[https://en.m.wikipedia.org/wiki/Median_absolute_deviation](https://en.m.wikipedia.org/wiki/Median_absolute_deviation)

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lonelappde
The link says Median Absolute Deviation.

Here's a SE discussion with people using the term inconsistently without even
noticing. [https://datascience.stackexchange.com/questions/42760/mad-
vs...](https://datascience.stackexchange.com/questions/42760/mad-vs-rmse-vs-
mae-vs-msle-vs-r%C2%B2-when-to-use-which)

It's absurd to use ambiguous acronyms like this.

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AnthonyLloyd
Happy to answer questions if anything is not clear or discuss.

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Lemaxoxo
Would you happen the memory complexity of this algorithm? I maintain an online
machine learning library written in Python, called creme, where we implement
online statistics. We have a generic onine algorithm for estimating quantiles,
and so a specific algorithm for estimating medians would be welcome. I'm
always on the lookout for such online algorithms.

~~~
AnthonyLloyd
It's a fixed memory size but gets released when you move into the recursive
part. Increasing the fixed part will give you a better starting estimate.

See here for quantiles: [https://stackoverflow.com/questions/1058813/on-line-
iterator...](https://stackoverflow.com/questions/1058813/on-line-iterator-
algorithms-for-estimating-statistical-median-mode-skewnes)

The P^2 algorithm used in creme is interesting. For the median it would give a
2 sided median deviation. Maybe this could be changed slightly to be symmetric
and give Median and MAD. I'll look into.

