3 ms·
Median and Mad Revisited with an Online Estimator
- AnthonyLloyd 7y agoHappy to answer questions if anything is not clear or discuss.
- Lemaxoxo 7y agoWould 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 7y agoIt'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-algorithms-for-estimating-statistical-median-mode-skewnes https://stackoverflow.com/questions/1058813/on-line-iterator... 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.
- lonelappde 7y agoWhat is MAD?
- AnthonyLloyd 7y agoMedian Absolute Deviation Discussed in the previous post: http://anthonylloyd.github.io/blog/2016/10/21/MAD-Outliers http://anthonylloyd.github.io/blog/2016/10/21/MAD-Outliers It's roughly the range around the median where half the sample is within (since you can do 2 sided MAD also).
- johnmyleswhite 7y agoCan you link to a proof of the equation starting at "The standard error of the sample Median approximates to"?
- AnthonyLloyd 7y agoIt's a quite hand wavy central limit theory for large N or close to normal distribution: http://davidmlane.com/hyperstat/A106993.html http://davidmlane.com/hyperstat/A106993.html
- asplake 7y agoMAD being mean absolute deviation https://en.m.wikipedia.org/wiki/Median_absolute_deviation https://en.m.wikipedia.org/wiki/Median_absolute_deviation
- lonelappde 7y agoThe 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-rmse-vs-mae-vs-msle-vs-r%C2%B2-when-to-use-which https://datascience.stackexchange.com/questions/42760/mad-vs... It's absurd to use ambiguous acronyms like this.