us VS t-digest

It might be easier to think about it as a stack, rather than a tree. Each element of the stack represents a subtree -- a perfect binary tree. If you ever have two subtrees of height k, you merge them together into one subtree of height k+1. Your stack might already have another subtree of height k+1; if so, you repeat the process, until there's at most one subtree of each height.

This process is isomorphic to binary addition. Worked example: let's start with a single leaf, i.e. a subtree of height 0. Then we "add" another leaf; since we now have a pair of two equally-sized leaves, we merge them into one subtree of height 1. Then we add a third leaf; now this one doesn't have a sibling to merge with, so we just keep it. Now our "stack" contains two subtrees: one of height 1, and one of height 0.

Now the isomorphism: we start with the binary integer 1, i.e. a single bit at index 0. We add another 1 to it, and the 1s "merge" into a single 1 bit at index 1. Then we add another 1, resulting in two 1 bits at different indices: 11. If we add one more bit, we'll get 100; likewise, if we add another leaf to our BNT, we'll get a single subtree of height 2. Thus, the binary representation of the number of leaves "encodes" the structure of the BNT.

This isomorphism allows you to do some neat tricks, like calculating the size of a Merkle proof in 3 asm instructions. There's some code here if that helps: https://github.com/lukechampine/us/blob/master/merkle/stack....

You could also check out section 5.1 of the BLAKE3 paper: https://github.com/BLAKE3-team/BLAKE3-specs/blob/master/blak...

This isn't what I'm asking for - I don't care if it's baked into us, exists as a backend for minio, uses PseudoKV https://github.com/lukechampine/us/issues/67, or whatever the case may be. I see no value in sending any third party my private data in an unencrypted form (uploading to your server, even if over HTTPS, you got my data).

> 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