What category theory teaches us about dataframes (mchav.github.io)

by mchav 65 comments 190 points
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65 comments

[−] rich_sasha 42d ago
The article starts well, on trying to condense pandas' gaziliion of inconsistent and continuously-deprecated functions with tens of keyword arguments into a small, condensed set of composable operations - but it lost me then.

The more interesting nugget for me is about this project they mention: https://modin.readthedocs.io/en/latest/index.html called Modin, which apparently went to the effort of analysing common pandas uses and compressed the API into a mere handful of operations. Which sounds great!

Sadly for me the purpose seems to have been rather to then recreate the full pandas API, only running much faster, backed by things like Ray and Dask. So it's the same API, just much faster.

To me it's a shame. Pandas is clearly quite ergonomic for various exploratory interactive analyses, but the API is, imo, awful. The speed is usually not a concern for me - slow operations often seem to be avoidable, and my data tends to fit in (a lot of) RAM.

I can't see that their more condensed API is public facing and usable.

[−] few 42d ago
I felt like one or two decades ago, all the rage was about rewriting programs into just two primitives: map and reduce.

For example filter can be expressed as:

  is_even = lambda x: x % 2 == 0
  mapped = map(lambda x: [x] if is_even(x) else [], data)
  filtered = reduce(lambda x, y: x + y, mapped, [])
But then the world moved on from it because it was too rigid
[−] pavodive 42d ago
When I started reading about pandas complexity and the smaller set of operations needed, couldn't help but think of R's data.table simplicity.

Granted, it's got more than 15 functions, but its simplicity seems to me very similar to what the author presented in the end.

[−] caseyross 42d ago
Interesting idea. I feel like it could be productive to categorize operations by their result shape as well:

- Row select: From N rows, produce 0-N rows.

- Column select: From N columns, produce 0-N columns.

- Table add: From MxN and OxP tables, produce max M+OxN+P table.

- Table subtract: From MxN and OxP tables, produce min 0x0 table.

This line of thinking reveals some normally hard-to-see similarities, such as groupby and dedupe sharing the same underlying mechanism. (i.e., both are "collapsing" row selects.)

[−] voxleone 42d ago
It’s almost suspiciously elegant: focus on transformations and their composition, and the structure takes care of itself.
[−] toxik 42d ago
Pandas and so on exist for the same reason Django's ORM and SqlAlchemy do: people do not want to string interpolate to talk to their database. SQL is great for DBA's, and absolutely sucks for programmers. Microsoft was really onto something with LINQ, in my opinion.
[−] getnormality 42d ago
Hmm. Folks trying to discover the elegant core of data frame manipulation by studying... pandas usage patterns. When R's dplyr solved this over a decade ago, mostly by respecting SQL and following its lead.

The pandas API feels like someone desperately needed a wheel and had never heard of a wheel, so they made a heptagon, and now millions of people are riding on heptagon wheels. Because it's locked in now, everyone uses heptagon wheels, what can you do? And now a category theorist comes along, studies the heptagon, and says hey look, you could get by on a hexagon. Maybe even a square or a triangle. That would be simpler!

No. Stop. Data frames are not fundamentally different from database tables [1]. There's no reason to invent a completely new API for them. You'll get within 10% of optimal just by porting SQL to your language. Which dplyr does, and then closes most of the remaining optimality gap by going beyond SQL's limitations.

You found a small core of operations that generates everything? Great. Also, did you know Brainfuck is Turing-complete? Nobody cares. Not all "complete" systems are created equal. A great DSL is not just about getting down to a small number of operations. It's about getting down to meaningful operations that are grammatically composable. The relational algebra that inspired SQL already nailed this. Build on SQL. Don't make up your own thing.

Like, what is "drop duplicates"? What are duplicates? Why would anyone need to drop them? That's a pandas-brained operation. You want the distinct keys defined by a select set of key columns, like SQL and dplyr provide.

Who needs a separate select and rename? Select is already using names, so why not do your name management there? One flexible select function can do it all. Again, like both SQL and dplyr.

Who needs a separate difference operation? There's already a type of join, the anti-join, that gets that done more concisely and flexibly, and without adding a new primitive, just a variation on the concept of a join. Again, like both SQL and dplyr.

Props to pandas for helping so many people who have no choice but to do tabular data analysis in Python, but the pandas API is not the right foundation for anything, not even a better version of pandas.

[1] No, row labels and transposition are not a good enough reason to regard them as different. They are both just structures that support pivoting, which is vastly more useful, and again, implemented by both R and many popular dialects of SQL.

[−] DangitBobby 42d ago
I guess I have pandas brain because I definitely want to drop duplicates, 100% of the time I'm worried about duplicates and 99% of the time the only thing I want to do with duplicates is drop them. When you've got 19 columns it's _really fucking annoying_ if the tool you're using doesn't have an obvious way to say select distinct on () from my_shit. Close second at say, 98% of the time, I want to a get a count of duplicates as a sanity check because I know to expect a certain amount of them. Pandas makes that easy too in a way SQL makes really fucking annoying. There are a lot of parts on pandas that made me stop using it long ago but first class duplicates handling is not among them.

And the API is vastly superior to SQL is some respects from a user perspective despite being all over the place in others. Dataframe select/filtering e.g. df = df[df.duplicated(keep='last')] is simple, expressive, obvious, and doesn't result in bleeding fingers. The main problem is the rest of the language around it with all the indentations, newlines, loops, functions and so on can be too terse or too dense and much hard to read than SQL.

[−] getnormality 42d ago
Duplicates in source data are almost always a sign of bad data modeling, or of analysts and engineers disregarding a good data model. But I agree that this ubiquitous antipattern that nobody should be doing can still be usefully made concise. There should be a select distinct * operation.

And FWIW I personally hate writing raw SQL. But the problem with the API is not the data operations available, it's the syntax and lack of composability. It's English rather than ALGOL/C-style. Variables and functions, to the extent they exist at all, are second-class, making abstraction high-friction.

[−] DangitBobby 42d ago
Oooh buddy how's the view from that ivory tower??

But seriously I'm not in always in control of upstream data, I get stuff thrown over to my side of the fence by an organization who just needs data jiggled around for one-off ops purposes. They are communicating to me via CSV file scraped from Excel files in their Shared Drive, kind of thing.

[−] getnormality 42d ago
Do what you gotta do, but most of my job for the past decade has been replacing data pipelines that randomly duplicate data with pipelines that solve duplication at the source, and my users strongly prefer it.

Of course, a lot of one-off data analysis has no rules but get a quick answer that no one will complain about!

[−] DangitBobby 42d ago
I updated my OG comment for context. As an org we also help clients come up with pipelines but it's just unrealistic to do a top-down rebuild of their operations to make one-off data exports appeal to my sensibilities.
[−] getnormality 42d ago
I agree, sometimes data comes to you in a state that is beyond the point where rigor is helpful. And for some people that kind of data is most of their job!
[−] doug_durham 42d ago
Duplicates are a sign of reality. Only where you have the resources to have dedicated people clean and organize data do you have well modeled data. Pandas is a power tool for making sense of real data.
[−] mamcx 42d ago

> Duplicates in source data are almost always a sign of bad data modeling

Nope. Duplicates in source data(INPUT) is natural, correct and MUST be supported or almost all data become impossible.

What is the actual problem is the OUTPUT. Duplicates on the OUTPUT need to be controlled and explicit. In general, we need in the OUTPUT a unique rowby a N-key, but probably not need it to be unique for the rest, so, in the relational model, you need unique for a combination of columns (rarely, by ALL of them).

[−] gregw2 42d ago
You articulate your case well, thank you!

I always warn people (particularly junior people) though that blindly dropping duplicates is a dangerous habit because it helps you and others in your organization ignore the causes of bad data quickly without getting them fixed at the source. Over time, that breeds a lot of complexity and inefficiency. And it can easily mask flaws in one's own logic or understanding of the data and its properties.

[−] getnormality 42d ago
On reflection I think it's possible I may have missed the potential positive value of the post a bit. Maybe analyzing pandas gets you down to a set of data frame primitives that is helpful to build any API. Maybe the API you start with doesn't matter. I don't know. When somebody works hard to make something original, you should try to see the value in it, even if the approach is not one you would expect to be helpful.

I stand by my warnings against using pandas as a foundation for thinking about tabular data manipulation APIs, but maybe the work has value regardless.

[−] gwerbin 42d ago

> There's no reason to invent a completely new API for them

Yes there is: SQL is one of many possible ways to interact with tabular data, why should it be the only one? R data frames literally pioneered an alternative API. Dplyr is fantastic for many reasons, one of those being that people like the verb-based approach

Furthermore I argue that dplyr is not particularly similar to SQL in the way you actually use it and how it's actually interpreted/executed.

As for the rest I feel like you're just stating your preferences as fact.

[−] jiehong 42d ago
[−] hermitcrab 42d ago

>a dataframe is a tuple (A, R, C, D): an array of data A, row labels R, column labels C, and a vector of column domains D.

What is 'a vector of column domains D'? A description of how the data A maps to columns?

[−] jeremyscanvic 42d ago
It's very insightful how they explain the difference between dataframes and SQL tables / standard relational structures!
[−] kiviuq 42d ago
there is also ZIO Prelude and ZIO schema...
[−] jmount 42d ago
I like this sort of study- but it really misses the point to not give more credit for some of the observations and designs to Codd and others.
[−] kokhanserhii 42d ago
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[−] Whyachi 42d ago
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[−] hermitcrab 42d ago
I guess this article is an interesting exercise from a pure maths point of view. But, as someone developing a drag and drop data wrangling tool the important thing is creating a set of composable operations/primitive that are meaningful and useful to your end user. We have ended up 73 distinct transforms in Easy Data Transform. Sure they overlap to an extent, but feel they are at the right semantic level for our users, who are not category theorists.