RT @jasonintrator@twitter.com

A few months ago, at the youthful age of 92, Noam Chomsky absolutely destroyed the Yale Political Union in debate (they were defending US Empire against him). Nothing was left standing, utter intellectual domination, ending with Chomsky abruptly signing off with, “I’m done here.”

🐦🔗: twitter.com/jasonintrator/stat

RT @Just1n14n@twitter.com

This is such a useful read for our current work on community detection on massive business networks. twitter.com/tiagopeixoto/statu

🐦🔗: twitter.com/Just1n14n/status/1

RT @kennardmatt@twitter.com

Happy 93rd birthday Noam Chomsky. He's inspired millions of people around the world, me included, to pick apart the useful ideologies that power uses to justify itself. He's a one-off. A moral and intellectual giant.

🐦🔗: twitter.com/kennardmatt/status

RT @dukelarby@twitter.com

I like to think I'm pretty jaded by now but seeing the Biden admin openly mocking the idea that they directly help Americans is gut wrenching. twitter.com/mkarolian/status/1

🐦🔗: twitter.com/dukelarby/status/1

RT @jacobin@twitter.com

Happy 93rd birthday to Noam Chomsky, one of the greatest and most principled public intellectuals the American left has ever produced.

🐦🔗: twitter.com/jacobin/status/146

RT @tiagopeixoto@twitter.com

New blog post!

"No free lunch in community detection?"

NFL theorems are tricky to interpret, and are often misunderstood.

No, it does not mean that all community detection algorithms are equally good. 1/9

(Based on arxiv.org/abs/2112.00183)

skewed.de/tiago/blog/free-lunc

🐦🔗: twitter.com/tiagopeixoto/statu

RT @niedakh@twitter.com

This paper by @tiagopeixoto@twitter.com is a must read for anyone working with networks.

arxiv.org/pdf/2112.00183.pdf

🐦🔗: twitter.com/niedakh/status/146

Man, don't make me feel bad for Yoko.

RT @mollygoggles@twitter.com

Don’t care about the Beatles documentary but I did learn that my brother thought everyone hates Yoko Ono because she shot John Lennon.

🐦🔗: twitter.com/mollygoggles/statu

RT @tiagopeixoto@twitter.com

New blog post!

"No free lunch in community detection?"

NFL theorems are tricky to interpret, and are often misunderstood.

No, it does not mean that all community detection algorithms are equally good. 1/9

(Based on arxiv.org/abs/2112.00183)

skewed.de/tiago/blog/free-lunc

🐦🔗: twitter.com/tiagopeixoto/statu

Does the NFL theorem tell us something important? YES!

It tells us that we need to be explicit about our inductive bias (i.e. what kind of problem we want to solve).

Compressibility is indeed an inductive bias, but one that relies only on Occam's razor, and nothing else! 9/9

Show thread

And we should not interpret the eventual improved accuracy of a method that tends to work poorly overall as a *necessary* outcome of the NFL theorem. 8/9

Show thread

So, we shouldn't use the NFL theorem to justify an algorithm ("it's as good as any other") — after all that argument would be valid even for trivial algorithms (e.g. same partition every time). 7/9

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Indeed, there is a "free lunch" with compressive problems, since some algorithms will work better than others!

Is there a universal algorithm that will work better in every compressive instance, or a majority? It's unclear!

But the NFL theorem tells us nothing about this. 6/9

Show thread

As soon as we limit ourselves to *compressive* problem instances, then we are out of scope of the NFL theorem.

Note that it is not necessary to specify *how* the problems are compressive (i.e. which model they come from), only that they can be compressed somehow. 5/9

Show thread

More formally, a partition is informative if its knowledge can be used to *compress* the network, i.e. describe it with fewer bits than if we did not know it.

Below is an example of a compressive problem instance.

Looks familiar? This is the kind of problem we have in mind. 4/9

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But what does that tell us about the problems we actually want to solve?

Can we make a general statement about what is an "interesting" community detection problem?

There is in fact, a very simple one: we require the partition to be *informative* of the network structure! 4/9

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What's strange about this example? Well, there's no community *structure*. It's just a random network with a random partition.

The vast majority of instances accounted by the NFL theorem look like this.

OK, so all algorithms perform equally "well" in these cases. 🤷‍♂️

3/9

Show thread

But what does "all problem instances" mean? For Leto et al, a problem instance is simply an arbitrary pairing of a network and a partition.

Any network, any partition.

How does such a typical problem instance look like?

We can see one below. 2/9

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