t-digest VS rolling-quantiles

> I get a lot of benefit from this information but somehow it feels shallow.

I take a longer view to this. For example, a few years ago I read about an algorithm to calculate percentiles in real time. [0]

It literally just came up at work today. I haven't used that information but maybe two times since I read it, but it was super relevant today and saved my team potential weeks of development.

So maybe it's not so shallow.

But to your actual question, I have a similar problem. The best I can say is that deadlines help. I usually put down the HN and Youtube when I have a deadline coming up. And not just at work. I make sure my hobbies have deadlines too.

I tell people when I think something will be done, so they start bugging me about it when it doesn't get done, so that I have a "deadline". Also one of my hobbies is pixel light shows for holidays, which come with excellent natural deadlines -- it has to be done by the holiday or it's useless.

So either find an "accountability buddy" who will hold you to your self imposed deadlines, or find a hobby that has natural deadlines, like certain calendar dates, or annual conventions or contests that you need to be done by.

[0] https://github.com/tdunning/t-digest

I am enamored by data structures in the sketch/summary/probabilistic family: t-digest[1], q-digest[2], count-min sketch[3], matrix-sketch[4], graph-sketch[5][6], Misra-Gries sketch[7], top-k/spacesaving sketch[8], &c.

What I like about them is that they give me a set of engineering tradeoffs that I typically don't have access to: accuracy-speed[9] or accuracy-space. There have been too many times that I've had to say, "I wish I could do this, but it would take too much time/space to compute." Most of these problems still work even if the accuracy is not 100%. And furthermore, many (if not all of these) can tune accuracy to by parameter adjustment anyways. They tend to have favorable combinatorial properties ie: they form monoids or semigroups under merge operations. In short, a property of data structures that gave me the ability to solve problems I couldn't before.

I hope they are as useful or intriguing to you as they are to me.

1. https://github.com/tdunning/t-digest

2. https://pdsa.readthedocs.io/en/latest/rank/qdigest.html

3. https://florian.github.io/count-min-sketch/

4. https://www.cs.yale.edu/homes/el327/papers/simpleMatrixSketc...

5. https://www.juanlopes.net/poly18/poly18-juan-lopes.pdf

6. https://courses.engr.illinois.edu/cs498abd/fa2020/slides/20-...

7. https://people.csail.mit.edu/rrw/6.045-2017/encalgs-mg.pdf

8. https://www.sciencedirect.com/science/article/abs/pii/S00200...

9. It may better be described as error-speed and error-space, but I've avoided the term error because the term for programming audiences typically evokes the idea of logic errors and what I mean is statistical error.

Ah, I misunderstood what you meant. If you are reporting static buckets I get how that is better than what folks typically do but how do you know the buckets a priori? Others back their histograms with things like https://github.com/tdunning/t-digest. It is pretty powerful as the buckets are dynamic based on the data and histograms can be added together.

Yes, but if you need to estimate median on the fly (e.g., over a stream of data) or in parallel there are better ways.

There are some newer data structures that take this to the next level such as T-Digest[1], which remains extremely accurate even when determining percentiles at the very tail end (like 99.999%)

[1]: https://arxiv.org/pdf/1902.04023.pdf / https://github.com/tdunning/t-digest

[2] https://github.com/tdunning/t-digest

T-Digest

This is pretty cool. The title would be a bit more descriptive if it were “Fast Rolling Quantile Filters for Python”, since the high-pass/low-pass filter functionality seems to be the focus.

The README mentions it uses binary heaps - if you’re willing to accept some (bounded) approximation, then it should be possible to reduce memory usage and somewhat reduce runtime by using a sketching data structure like Dunning’s t-digest: https://github.com/tdunning/t-digest/blob/main/docs/t-digest....

There is an open source Python implementation, although I haven’t used it and can’t vouch for its quality: https://github.com/CamDavidsonPilon/tdigest

Not sure about the parent post, but I also wrote a Python package inspired by a past interview question! It uses a pair of heaps to keep track of items in a time-series window and find exact quantile estimates.

https://github.com/marmarelis/rolling-quantiles