I guess? I mean, there’s three separate degrees of “should really be kept contained”-ness here:
Category theory → string diagrams, which pretty much everyone keeps contained, including people who know the actual category theory
String diagrams → Bayes nets, which is pretty straightforward if you sit and think for a bit about the semantics you accept/are given for string diagrams generally and maybe also look at a picture of generators and rules—not something anyone needs to wrap up nicely but it’s also a pretty thin
[Causal theory/Bayes net] string diagrams → actual statements about (natural) latents, which is something I am still working on; it’s turning out to be pretty effortful to grind through all the same transcriptions again with an actually-proof-usable string diagram language this time. I have draft writeups of all the “rules for an algebra of Bayes nets”—a couple of which have turned out to have subtleties that need working out—and will ideally be able to write down and walk through proofs entirely in string diagrams while/after finishing specifications of the rules.
So that’s the state of things. Frankly I’m worried and generally unhappy about the fact that I have a post draft that needs restructuring, a paper draft that needs completing, and a research direction to finish detailing, all at once. If you want some partial pictures of things anyway all the same, let me know.
I just meant the “guts of the category theory” part. I’m concerned that anyone says that it should be contained (aka used but not shown), and hope it’s merely that you’d expect to lose half the readers if you showed it. I didn’t mean to add to your pile of work and if there is no available action like snapping a photo that takes less time than writing the reply I’m replying to did, then disregard me.
The phrasing I got from the mentor/research partner I’m working with is pretty close to the former but closer in attitude and effective result to the latter. Really, the major issue is that string diagrams for a flavor of category and commutative diagrams for the same flavor of category are straight-up equivalent, but explicitly showing this is very very messy, and even explicitly describing Markov categories—the flavor of category I picked as likely the right one to use, between good modelling of Markov kernels and their role doing just that for causal theories (themselves the categorification of “Bayes nets up to actually specifying the kernels and states numerically”) - is probably too much to put anywhere in a post but an appendix or the like.
...if there is no available action like snapping a photo that takes less time than writing the reply I’m replying to did...
There is not, but that’s on me. I’m juggling too much and having trouble packaging my research in a digestible form. Precarious/lacking funding and consequent binding demands on my time really don’t help here either. I’ll add you to the long long list of people who want to see a paper/post when I finally complete one.
I guess a major blocker for me is—I keep coming back to the idea that I should write the post as a partially-ordered series of posts instead. That certainly stands out to me as the most natural form for the information, because there’s three near-totally separate branches of context—Bayes nets, the natural latent/abstraction agenda, and (monoidal category theory/)string diagrams—of which you need to somewhat understand some pair in order to understand major necessary background (causal theories, motivation for Bayes net algebra rules, and motivation for string diagram use), and all three to appreciate the research direction properly. But I’m kinda worried that if I start this partially-ordered lattice of posts, I’ll get stuck somewhere. Or run up against the limits of what I’ve already worked out yet. Or run out of steam with all the writing and just never finish. Or just plain “no one will want to read through it all”.
give me the guts!!1
don’t polish them, just take a picture of your notes or something.
I guess? I mean, there’s three separate degrees of “should really be kept contained”-ness here:
Category theory → string diagrams, which pretty much everyone keeps contained, including people who know the actual category theory
String diagrams → Bayes nets, which is pretty straightforward if you sit and think for a bit about the semantics you accept/are given for string diagrams generally and maybe also look at a picture of generators and rules—not something anyone needs to wrap up nicely but it’s also a pretty thin
[Causal theory/Bayes net] string diagrams → actual statements about (natural) latents, which is something I am still working on; it’s turning out to be pretty effortful to grind through all the same transcriptions again with an actually-proof-usable string diagram language this time. I have draft writeups of all the “rules for an algebra of Bayes nets”—a couple of which have turned out to have subtleties that need working out—and will ideally be able to write down and walk through proofs entirely in string diagrams while/after finishing specifications of the rules.
So that’s the state of things. Frankly I’m worried and generally unhappy about the fact that I have a post draft that needs restructuring, a paper draft that needs completing, and a research direction to finish detailing, all at once. If you want some partial pictures of things anyway all the same, let me know.
I just meant the “guts of the category theory” part. I’m concerned that anyone says that it should be contained (aka used but not shown), and hope it’s merely that you’d expect to lose half the readers if you showed it. I didn’t mean to add to your pile of work and if there is no available action like snapping a photo that takes less time than writing the reply I’m replying to did, then disregard me.
The phrasing I got from the mentor/research partner I’m working with is pretty close to the former but closer in attitude and effective result to the latter. Really, the major issue is that string diagrams for a flavor of category and commutative diagrams for the same flavor of category are straight-up equivalent, but explicitly showing this is very very messy, and even explicitly describing Markov categories—the flavor of category I picked as likely the right one to use, between good modelling of Markov kernels and their role doing just that for causal theories (themselves the categorification of “Bayes nets up to actually specifying the kernels and states numerically”) - is probably too much to put anywhere in a post but an appendix or the like.
There is not, but that’s on me. I’m juggling too much and having trouble packaging my research in a digestible form. Precarious/lacking funding and consequent binding demands on my time really don’t help here either. I’ll add you to the long long list of people who want to see a paper/post when I finally complete one.
I guess a major blocker for me is—I keep coming back to the idea that I should write the post as a partially-ordered series of posts instead. That certainly stands out to me as the most natural form for the information, because there’s three near-totally separate branches of context—Bayes nets, the natural latent/abstraction agenda, and (monoidal category theory/)string diagrams—of which you need to somewhat understand some pair in order to understand major necessary background (causal theories, motivation for Bayes net algebra rules, and motivation for string diagram use), and all three to appreciate the research direction properly. But I’m kinda worried that if I start this partially-ordered lattice of posts, I’ll get stuck somewhere. Or run up against the limits of what I’ve already worked out yet. Or run out of steam with all the writing and just never finish. Or just plain “no one will want to read through it all”.