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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.

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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...

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.

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