general · deprecated: statistics reading group

@Oliver Shetler , would it be possible for you to keep us informed when you assemble such a reading group? I have a few papers I'd like to read as well and it would be good to have a back and forth discussion amongst those with different backgrounds so that things could move more efficiently. I can't promise I'll devote myself fully, but there's a reasonable chance I can due to the immense overlap of interest here.

Oliver Shetler (Jun 09 2020 at 10:04):

Interesting that you would mention this right now. I'm actually sitting here working on my statement of motivation for the reading circle. I'm a bit swamped with classes for the next four weeks, but I'll probably announce the first meeting before the end of the month.

Oliver Shetler (Jun 09 2020 at 10:21):

Can you enumerate the papers you have in mind? I'll put them into my reading list and mark them with your preference.

Arthur Parzygnat (Jun 09 2020 at 20:03):

@Oliver Shetler Yes. Many of these were papers mentioned during the workshop on categorical probability that we both attended. Here are some of them, not written in any particular order (Note: I don't know if I actually want to go through all of these---I am just listing ones that I believe are either interesting or important based on the discussions from the workshop).

Notification Bot (Jun 10 2020 at 04:52):

Oliver Shetler (Jun 10 2020 at 20:11):

I agree that McCullaugh is the obvious first paper to read. Here is an extended list, in no particular order (except McCullaugh which we agree should be at the top).

Fritz - "A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics"

Keimel – "The Monad of Probability Measures over Compact Ordered Spaces and its Eilenberg-Moore Algebras"

Perrone – "Categorical Probability and Stochastic Dominance in Metric Spaces" (Pd.D. Thesis)

Patterson – "The Algebra and Machine Representation of Statistical Models" (Ph.D. Thesis)

Fritz and Perrone – "A Probability Monad as the Colimit of Spaces of Finite Samples"

Jacobs and Furber – "Towards a Categorical Account of Conditional Probability"

Jacobs – "Parameters and Parameterization in Specification, using Distributive Categories"

Parzygnat – "Inverses, Disintegrations, and Bayesian Inversion in Quantum Markov Categories"

_____I've set out these papers as possible supplemental readings that are not categorical._____

Dawid and Studeny - "Conditional Products - An Alternative Approach to Conditional Independence"

Wald - "Contributions to the Theory of Statistical Estimation and Testing Hypotheses"

Oliver Shetler (Jun 10 2020 at 20:14):

I'm going to take a closer look at abstracts and rate each paper for its potential as educational material, rather than for other qualities. The focus should be on if it introduces important general concepts and if it has clear pedagogy. If others want to do the same, either rate the papers for educational value on a scale from 1-10 or just list the top 3-5 options in your mind.

Oliver Shetler (Jun 10 2020 at 20:15):

Additional papers are welcome as well. We don't need to read all of them, but having a list of the important papers in this very young field could be helpful to everybody.

Oliver Shetler (Jun 10 2020 at 20:19):

I'm thinking that after McCallaugh, we should take a look at Patterson's thesis and something on Markov Categories and probability monads soon thereafter. It also seems like Jacobs has done some interesting work on parameter learning. These are just some preliminary thoughts though.

Oliver Shetler (Jun 10 2020 at 20:21):

Additionally, if enough people are unfamiliar with statistics, I can provide relevant practice problems from an introductory Statistics textbook for people to work on as concepts come up.

John Baez (Jun 10 2020 at 21:30):

I like this reading list! If I can't go to the group I should at least browse the papers.

Fabrizio Genovese (Jun 10 2020 at 21:51):

This reading group sounds really interesting indeed. I'd like to participate as soon as it starts :slight_smile:

Arthur Parzygnat (Jun 10 2020 at 22:17):

Since I've actually been reading Jacobs' papers, this would be excellent. I'm actually currently going through his paper on Conjugate Priors, which discusses Bayesian updating and parametric Bayes (and I have actually been acquiring some questions with regards to that paper, which could form a nice discussion).
I agree that one should start with things that are easier to read and address simpler ideas before moving on to more advanced topics. Personally, I can say with confidence (only based on the fact that I've read many of their papers!) that anything written by Fritz, Perrone, Fong, and Jacobs is well-written (in the sense that it is not only accessible but also precise, not overly technical, and contains examples one can check their understanding with). The top five papers I recommend (the first four are purely based on me having read parts of them and knowing that the material is solid and reasonably accessible) are:

Joshua Tan (Jun 10 2020 at 22:22):

Oliver Shetler (Jun 10 2020 at 23:32):

Yes, I'm putting one together. We'll probably start regular meetings next month. I'll post the details here and on the NYC Category Theory meetup.com group. I'll also see about announcing it on the Azimuth forum. If there's enough interest, we may take a poll of goals and split into circles. If we do that, I'll try to weave meetings so that people from separate circles with separate goals still interact.

John Baez (Jun 10 2020 at 23:36):

I've already advertised the general idea of the reading group, and especially that nice reading list, on the Azimuth Forum. So, whenever you write an announcement with details, let me know.

John Baez (Jun 10 2020 at 23:39):

By the way, if you or anyone has the energy to add links to this list, that would get a lot more people to look at these papers. I'll do the first one, to show what I mean:

• McCullagh: "[What is a statistical model?](https://projecteuclid.org/euclid.aos/1035844977)"

• Morse and Sacksteder, "Statistical isomorphism"

• Simpson, "Probability sheaves and the Giry monad"

• Fritz, "A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics"

• Jacobs, "Probabilities, distribution monads, and convex categories"

• Keimel, "The Monad of probability measures over compact ordered spaces and its Eilenberg--Moore algebras"

• McCullaugh, Di Nardo, Senato, "Natural statistics for spectral samples"

• Perrone, *Categorical Probability and Stochastic Dominance in Metric Spaces* (Ph.D. Thesis)

• Patterson, *The Algebra and Machine Representation of Statistical Models* (Ph.D. Thesis)

• Tuyeras, "A category theoretical argument for causal inference"

• Culbertson and Sturtz, "A categorical foundation for Bayesian probability"

• Fong, "Causal theories: a categorical perspective on Bayesian networks"

• Fritz and Perrone, "A probability monad as the colimit of spaces of finite samples"

• Fritz and Perrone, "Bimonoidal structure of probability monads"

• Fritz, "A presentation of the category of stochastic matrices"

• Jacobs and Furber, "Towards a categorical account of conditional probability"

• Bradley, *At the Interface of Algebra and Statistics* (Ph.D. Thesis)

• Bradley, Stoudenmire and Terilla, "Modeling sequences with quantum states"

• Jacobs, "Categorical aspects of parameter learning"

• Jacobs, "Parameters and parameterization in specification, using distributive categories"

• Parzygnat, "Inverses, disintegrations, and Bayesian inversion in quantum Markov categories"

John Baez (Jun 10 2020 at 23:40):

I spend a lot of time adding links to things, but I'm too tired for this right now!

Oliver Shetler (Jun 10 2020 at 23:41):

I'm still groping my way through basic texts on CT such as Roman's Introduction to the Language of Category Theory, which means that I'm still at a very different level from most of you. On the other hand, I'm probably just competent enough at Probability and Statistics to help guide people who never studied it or forgot most of it.

I'll be trying to attract people from both the general pool at meetup.com, etc. and people from here. There may be wide variance in peoples' prior level of experience in both CT and probability / statistics.

Do you think it would still be rewarding for the more advanced people to go at the pace of the lowest common denominator? (likely me) If not, do you have any thoughts about how we might get the ball rolling for everybody while accommodating differing backgrounds?

Oliver Shetler (Jun 11 2020 at 00:14):

I should really make a prober bibliographic list, since this is the germ of my lit review anyway. Here's the links though. I also started but didn't finish a list of author websites

McCullagh, "[What is a statistical model?](https://projecteuclid.org/euclid.aos/1035844977)"

Morse and Sacksteder - "[Statistical isomorphism](https://projecteuclid.org/download/pdf_1/euclid.aoms/1177699610)"

Simpson - "[Probability Sheaves and the Giry Monad](https://drops.dagstuhl.de/opus/volltexte/2017/8051/pdf/LIPIcs-CALCO-2017-1.pdf)"

Fritz - "[A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics](https://arxiv.org/pdf/1908.07021v4.pdf)"

Jacobs – "[Probabilities, Distribution Monads, and Convex Categories](http://www.cs.ru.nl/B.Jacobs/PAPERS/triangle.pdf)"

Keimel, "[The Monad of Probability Measures over Compact Ordered Spaces and its Eilenberg-Moore Algebras](https://www.sciencedirect.com/science/article/pii/S0166864108002496)"

McCullaugh, Di Nardo, Senato – "[Natural Statistics for Spectral Samples](https://projecteuclid.org/download/pdfview_1/euclid.aos/1369836967)"

Perrone, "[Categorical Probability and Stochastic Dominance in Metric Spaces](http://www.paoloperrone.org/phdthesis.pdf)" (Pd.D. Thesis)

Patterson, "[The Algebra and Machine Representation of Statistical Models](https://www.epatters.org/assets/thesis.pdf)" (Ph.D. Thesis)

Tuyeras, "[A Category Theoretical Argument for Causal Inference](https://arxiv.org/pdf/2004.09999.pdf)"

Culbertson and Sturtz, "[A Categorical Foundation for Bayesian Probability](https://arxiv.org/pdf/1205.1488.pdf)"

Fong, "[Causal Theories: A Categorical Perspective on Bayesian Networks](https://arxiv.org/pdf/1301.6201.pdf)"

Fritz and Perrone, "[A Probability Monad as the Colimit of Spaces of Finite Samples](http://www.tac.mta.ca/tac/volumes/34/7/34-07.pdf)"

Fritz and Perrone, "[Bimonoidal Structure of Probability Monads](https://arxiv.org/pdf/1804.03527.pdf)"

Fritz, "[A Presentation of the Category of Stochastic Matrices](https://arxiv.org/pdf/0902.2554.pdf)"

Jacobs and Furber, "[Towards a Categorical Account of Conditional Probability](https://arxiv.org/pdf/1306.0831.pdf)"

Bradley, "[At the Interface of Algebra and Statistics](https://arxiv.org/pdf/2004.05631.pdf" (Ph.D. Thesis)

Bradley, Stoudenmire and Terilla – "[Modeling Sequences with Quantum States](https://arxiv.org/pdf/1910.07425.pdf)"

Jacobs, "[Categorical Aspects of Parameter Learning](https://arxiv.org/abs/1810.05814)"

Jacobs, "[Parameters and Parameterization in Specification, using Distributive Categories](http://www.cs.ru.nl/B.Jacobs/PAPERS/FI95.ps)"

Tuyeres, "[Category Theory for Genetics I: Mutations and Sequence Alignments](http://tac.mta.ca/tac/volumes/33/40/33-40.pdf)"

Parzygnat, "[Inverses, Disintegrations, and Bayesian Inversion in Quantum Markov Categories](https://arxiv.org/pdf/2001.08375.pdf)"

Jacobs, "[A Channel-Based Perspective on Conjugate Priors](https://arxiv.org/pdf/1707.00269.pdf)"

_____NON_CATEGORICAL_PAPERS______

Dawid and Studeny - "Conditional Products - An Alternative Approach to Conditional Independence"

Dawid - "Conditional independence in statistical theory"

Wald - "Contributions to the Theory of Statistical Estimation and Testing Hypotheses"

Huber - "Robust Estimation of a Location Parameter"

Fisher - "Moments and Product Moments of Sampling Distributions"

_____AUTHOR_PUBLICATION_SITES_____
[Jacobs, Bart](http://www.cs.ru.nl/~bart/PAPERS/index.html)
[Bradley, Tai-Danae](https://www.math3ma.com)
[Patterson, Evan](https://www.epatters.org/papers/#2020-thesis)
... (needs to be filled out)

John Baez (Jun 11 2020 at 00:43):

Evan Patterson (Jun 11 2020 at 00:46):

Thanks Arthur and Oliver for putting together this nice list of papers. I'd also like to participate in the reading group.

Oliver Shetler (Jun 11 2020 at 00:49):

When you get a chance, if you have any papers to add, and if you have a top three to five list (of papers you want to read) with some commentary, I'd like to hear your input.

Arthur Parzygnat (Jun 11 2020 at 05:43):

@Oliver Shetler I don't think it will disadvantage anybody. However, expect that we will take our time with things, but also expect that what we do learn, we will learn it very well (I would prefer this pace as opposed to just breezing through material and half-learning it). I suggest that if we focus on a paper that is heavy on the CT but light on the prob/stat, that we supplement as many categorical ideas with those from prob/stat as possible (and vice versa). Since I have experience with CT, I would be able to tell how much CT background a specific paper requires, and since you have some prob/stats background, you'll be able to do something similar on your end (and similarly others who join). This will also help us isolate papers with less required background so that we can start with those.

Oliver Shetler (Jun 11 2020 at 10:43):

That sounds like a reasonable plan. I like the idea of deliberatively articulating the requisite concepts for papers. That should make it possible for people to seek supplemental readings and ask coherent background questions in places where they might get lost. Since everybody seems to agree that McCullaugh is a good place to start, that simplifies the issue of sifting through papers for ease. We can look for requisite concepts for McCullaugh that need explaining, and then find then check to see if there are better expositions in other papers. Also people are willing to go slow, we can devise exercises for ourselves to really flesh out the concepts––especially with an eye to clarifying how these concepts can contribute to applications that CT is especially suited for such as NLP, causal models, biostatistics, etc.

Oliver Shetler (Jun 11 2020 at 10:51):

As for scheduling, do Saturdays generally work for everybody reading this? If so, I'm thinking we can do our first meeting on the 27th, so people have time to fit it into their schedules. This one will require little to no preparation. We'll just see who shows up and discuss some of what's been said here. I don't want to officially commit to reading any particular paper first until we've heard from the people who actually show up. Maybe there are better introductions to the topic, even if McCullough's paper is in everybody top five reading list. Then we can do first proper discussion meeting on the 11th. After that, we can decide whether people would prefer to do meetings every week or every other week. (My preference would be to do weekly meetings in July, but then scale back to every other week in August / September to accommodate many peoples' return to the Fall academic schedule, but we'll cross that bridge when we get there).

Morgan Rogers (he/him) (Jun 11 2020 at 11:12):

Please keep a permanent (perhaps communal) record of the exercises you come up with, and exercises from books that someone finds valuable to their understanding. Someone in this group will need/want to teach this subject sooner or later, and that record will be invaluable.

Oliver Shetler (Jun 11 2020 at 21:02):

I'll collect and organize exercises / notes that people happen to make on their own, and we can set a goal of writing out at least one explanation of one concept at every meeting. That's the sort of easy concrete outcome that makes regular meetings feel both manageable and worth it.

Bradley Saul (Jun 12 2020 at 12:43):

Joshua Tan (Jun 12 2020 at 17:41):

Joshua Tan (Jun 12 2020 at 17:42):

Oliver Shetler (Jun 12 2020 at 22:21):

I'll be announcing it on meetup.com soon and I'll post the link when I do. Additionally, I think @John Baez posted the document list with links to all the papers on the Azimuth forum. As for an organizing doc, I think an Overleaf Project would be the way to go, unless people have other ideas. I'll start it off with the list of papers and we can expand it from there. I've just got a busy weekend. My wife is moving to Seattle for her job, so I'm helping her with that. I'll put things up this Monday.

Oliver Shetler (Jun 12 2020 at 22:26):

In the mean time, please post any papers that you like that aren't on the list here. Also, any thoughts, suggestions, or questions you have. For example, you could say which of the papers on (or off) the list are in your top three to five personal agenda and you can say what your motivation is for wanting to apply Category Theory to Statistics and Probability.

Nathaniel Virgo (Jun 13 2020 at 01:38):

I'd like to join too, if the meetings happen to be at a Japan-compatible time. If they're not, I might try to read along anyway and participate via Zulip.

Arthur Parzygnat (Jun 13 2020 at 08:14):

I would agree with the suggestion of using an overleaf as a means for everybody compiling their understanding, examples, etc.

John Baez (Jun 13 2020 at 15:33):

I gave it this somewhat inaccurate tongue-in-cheek title to attract category theorists and repel statisticians who'd expect this is a course on category theory for statisticians.

John Baez (Jun 13 2020 at 15:34):

By the way, we now have access to a wiki, set up by @David Tanzer, and that's a good way to organize things.

John Baez (Jun 13 2020 at 15:37):

This is an applied category theory wiki that lets you use some TeX and also TikZ.

David Tanzer (Jun 14 2020 at 10:46):

@Oliver Shetler @John Baez
Yes, we're live - see the announcement I made under practice: communication for details.

David Tanzer (Jun 14 2020 at 10:49):

I created a page for Reading groups in the main web. @Oliver Shetler there you will see a page-creation link for a Statistics reading group - you've got the power.

Joshua Meyers (Jun 14 2020 at 13:03):

Oliver Shetler (Jun 14 2020 at 13:39):

I think he just meant that the wiki-page is live. I added the reading list, and I'm working on a little more content there.

Oliver Shetler (Jun 14 2020 at 13:46):

John Baez (Jun 19 2020 at 19:02):

By the way, I hope whoever is organizing the reading group - @Oliver Shetler? - has a good plan for running it. There may be lots of people at the first meeting, and if everyone just talks randomly, in proportion to how much they like to talk, it will be chaotic and boring, dominated by the loudest loudmouths.

John Baez (Jun 19 2020 at 19:04):

I think will work better if the discussion is well-organized - e.g. going through a list of topics, having some rules for how much people get to talk and when, etc. There are lots of possible organizations, but "winging it" is probably not one of the better ones.

John Baez (Jun 19 2020 at 19:05):

John Baez (Jun 19 2020 at 19:06):

Evan Patterson (Jun 19 2020 at 19:50):

Not sure how Oliver plans to run the meeting, but you can see the registered attendees at the event listing. Currently 19 people are registered.

Oliver Shetler (Jun 19 2020 at 22:04):

@John Baez, thank you for raising your concern about this. Any advice you have would be helpful. In my past reading groups, I've always had book exercises as a mechanism to reign people in. Clearly, this is a different situation. You are much more experienced with organizing meetings and you're good at it (you did a great job with Bradley's presentation, for example).

I'll tell you what the first meeting's goals are and, if you have time, you can reciprocate with some concrete suggestions.

This first meeting is just to discuss group goals / interests, order the papers in priorety, and decide what to read first. I'm hoping to keep the meeting to a maximum range of 1-2 hours.

I was thinking of going through the abstracts or table of contents for each paper and asking people to write down and report any topics or headings that seem especially important to them. I would keep a tally of these to get a sense of peoples' interests and goals.

Then I was thinking we'd try to build a consensus on which paper to tackle first.

Finally, I if there's time, I was thinking that we'd try and pick out one important concept from our paper of choice to focus in on for the next meeting.

I am also thinking of having people each briefly introduce themselves and explain their motivation for coming to the reading group, but I'm on the fence about this because I don't know how many "talkers" will attend. Maybe you have some advice on how to manage this and the above scenarios so things run smoothly?

Finally, I've set up the sign-up process to ask people why they are interested in applying Category Theory to Statistics. I am planning to use these answers, and the tally from the first meeting to privately outline a rough roadmap of topics to cover. (Who shows up to later meetings will also impact this).

As for future meetings, I'm hoping that each meeting will involve zeroing in on a specific concept from the paper and writing up brief notes on it, then deciding on the topic for the next meeting. Does that sound like a good plan, or are there better ways to organize paper-based reading groups? What have your experiences generally been like?

Oliver Shetler (Jun 19 2020 at 22:14):

Also, any volunteers to co-organize or help organize would be greatly appreciated. I felt like @Arthur Parzygnat was leaning into helping out but I don't want to assume / impose. Any help from anyone is very welcome :pray:

Arthur Parzygnat (Jun 20 2020 at 06:32):

@Oliver Shetler , it looks like your ideas for the first meeting seem very reasonable. I would follow exactly those ideas, but also allocate an amount of time for them. I haven't signed up via the meetup, but maybe I should because I plan on attending. And maybe the meetings should only be accessible to those who have signed up? (To get those that are a bit more serious)
As for co-organizing, I'd honestly prefer being one of the more active members than someone who helps with the organization. I can also advise. But yeah, I find the thought of being responsible for organizing is a bit stressful to me, so I'd prefer not to be an official part of that.
I wouldn't be too concerned about John's message/warning. If people drop out after the first meeting, that's fine. A reading/learning seminar can be haphazard, and that's honestly okay in my opinion. It's important not to stress yourself out. If you want, you can get some of the more serious participants (me, maybe Evan? etc) to help you out with a head start. For example, if we're discussing abstracts in the first meeting, some of us can volunteer to read them ahead of time and guide those discussions. (For example, I chose 5 papers for my top 5, and I can talk about why I chose those briefly).

Oliver Shetler (Jun 20 2020 at 13:31):

@Arthur Parzygnat thanks for the feedback. That all sounds perfectly reasonable. You're right about the attendance thing. In my experience, as many as 20 people can show up at the first meeting and then it can drop to as little as 2 or 3, even if everybody claims they had a great time. I'm not too worried about that. No big expectations here.

Also, I think it's totally fine if people who don't sign up show up. I don't care about "unserious" people showing up. People self-filter. No need for exclusivity. Sometimes people just have different attitudes towards signups. In fact, I had one serious attendee who refused to make a meetup account the entire time, but he attended every week for months.

As for the time limit idea, here's my concrete plan (these notes are as much for my reference as yours). For each abstract, and outline, I'll read it out loud to the group. As I do so, I'll ask people to write out a list of the highlights that stand out to them and post it on a thread in Zulip so I can review it later (that'll impose a natural time limit because we won't verbally discuss it). Then I'll ask people to list 3 articles they wouldn't mind starting with. Then we'll take like 5-15 minutes to pick one. Then we'll take 20 minutes to enumerate all the major concepts in that article and review the highlights people posted for it. We'll pick the first concept and assign a small number of pages for reading. We can save formal introductions for the second meeting, when the self-filtering has begun.

Lastly, no worries about helping to organize. For me, it serves as a mechanism to keep me reading, but it's not everybody's cup of tea. I think if you (and as you mentioned, @Evan Patterson, if he's willing, or anybody else who might volunteer) could take a look at the abstracts in advance, that would be very helpful though. For me, this first meeting will take place right before 2 exams and a final project in my final week of summer classes, so I'd prefer to keep my role purely to moderator until the next meeting. It would be very helpful if some people read ahead.

John Baez (Jun 20 2020 at 21:31):

Yes! I was warning him to be ready for a large number of not-necessarily-serious people who may show up at the first meeting; it takes a little skill to run a meeting with > 20 people. It will become easier when those people drop out.

John Baez (Jun 20 2020 at 21:33):

I bet more than 20 people will attend, so if each person explains their motivation for 1.5 minutes that will take half an hour. I'm not personally interested in spending half an hour on this, but if you are that's fine. One option is to do this on the second meeting.

John Baez (Jun 20 2020 at 21:35):

I guess this question is important: are you expecting people to look at McCullagh's paper before the first meeting, or not? It's not clear from anything you've sent out.

John Baez (Jun 20 2020 at 21:37):

If not, the first meeting will probably be mainly "organizational" in character. You could however do a great service by walking people through the key points of McCullagh's paper - or planning ahead of time to have someone else do this, someone who knows the paper well. That would help people read the paper and talk about it next time.

John Baez (Jun 20 2020 at 21:38):

John Baez (Jun 20 2020 at 21:39):

John Baez (Jun 20 2020 at 21:40):

So >20 people will list 3 papers each? That will take about 20 minutes if you included the usual friction. Something like a Doodle poll might be better.

John Baez (Jun 20 2020 at 21:42):

By the way, I thought you'd planned to start with McCullagh's paper. There are advantages to just asserting something like this, at first, instead of hoping for a couple dozen people who just met each other to make a group decision. Most of us are hoping you'll take charge, at least at first. You could say "Let me start by walking you through McCullagh's paper, since it tackles the fundamental question of what's a statistical model" - and then people could comment on that, etc.

John Baez (Jun 20 2020 at 21:45):

If I look like I'm trying to take charge, I'm honestly not. I'm just hoping you will, so I'm offering suggestions of what that could look like: decisive action instead of long processes where > 20 people all do something.

Later, when the group shrinks down to a nucleus of people who are strongly committed, it'll make sense for it become more informal, because people will know each other better and have more a sense of collective purpose.

Btw, I'm not sure I'll be in that nucleus. Feel free to disregard what I'm saying and do whatever you want.

Oliver Shetler (Jun 20 2020 at 23:02):

I value your advice because you know what you're doing _and_ I'm capable of taking things under advisement so don't worry about that.

John Baez (Jun 20 2020 at 23:11):

Oliver Shetler (Jun 20 2020 at 23:11):

I'm not expecting this. My assessment is that McCullough's paper is the authoritative work on statistical models, but it isn't the only possible starting point. I see two possible alternative starting points.

First, there might be expository sections in other papers that would serve as a good first introduction to some of McCullough's ideas (I think @Evan Patterson's thesis might have some good introductory materials, for example).

Second, a degree in statistics starts with probability theory, not statistical models. Therefore, it _might_ be better to start with Markov Categories or some other probability-based paper.

We will do McCullough either first or second. That much I'm comfortable committing to. But I wanted to leave some options open. It the default decision if people fail to decide though.

Andrew Shulaev (Jun 20 2020 at 23:16):

Just to clarify, by Markov Categories paper do you mean "Inverses, disintegrations, and Bayesian inversion inquantum Markov categories"?

Oliver Shetler (Jun 20 2020 at 23:17):

John Baez (Jun 20 2020 at 23:18):

Oliver Shetler (Jun 20 2020 at 23:18):

We could also start with something like Jacobs – “Probabilities, Distribution Monads, and Convex Categories”. I just meant we might start with a probability-based paper.

Andrew Shulaev (Jun 20 2020 at 23:20):

Yeah, I had that suspicion; but it was the only paper name that mentioned Markov categories in the title since I haven't looked deeper into them yet

Oliver Shetler (Jun 20 2020 at 23:34):

I'm thinking of basically putting each paper up on screen-share and asking people to note the parts they like. Maybe reading out loud isn't the best approach though. The idea is that everybody can look at the same thing at the same time and dump their impressions into a Zulip thread. I'm hoping to use that as a way of getting a feel for the highlights of each paper (according to the group).

eric brunner (Jun 21 2020 at 22:11):

i found evan patterson's thesis interesting, and appreciate the rest of the reading list.

Andrea Stine (she) (UCR) (Jun 23 2020 at 11:32):

I was planning on reading McCullagh's paper on my own already, so for me it seems like a natural starting place. I also think that while I learned statistics starting with probability theory, one of my undergraduate professors teaches his statistics courses starting with statistical models and I prefer that approach more, if for no other reason than it gives a goal to built up the probability theory toward.
As another comment, given that we can expect a pretty high disengagement rate between the first and second meetings, I personally would rather have all personal preferences stuff and whatnot be reserved for a Doodle poll per John's suggestion. Getting a taste for what we're reading instead seems more valuable to me.

Oliver Shetler (Jun 23 2020 at 19:09):

Hi @Andrea Stine (she) (UCR), if you're not interested in the housekeeping, no worries. Just show up on the 11th for our first proper reading group meeting. The assigned reading and goals will be posted after the first meeting.

Oliver Shetler (Jun 23 2020 at 19:11):

If I had decided to approach this by just assigning readings, that's when I would have scheduled the first meeting anyway. This meeting is just to gather qualitative data and get peoples' input on some things.

Oliver Shetler (Jun 23 2020 at 19:25):

I created a meetup event for the above meeting, for anyone who would prefer to start with that date.

Andrea Stine (she) (UCR) (Jun 25 2020 at 04:59):

Ok, cool! Given that, I'll probably still pop in on the first meeting, then, but I appreciate the clarification.

Oliver Shetler (Jun 25 2020 at 06:02):

Andrew Shulaev (Jun 26 2020 at 17:15):

I've been reading introductory chapters in Patterson's thesis and got really lost on monoidal categories, anyone has suggestions on what I can read to get up to speed? Preferrably something with exercises.
For the context I think I have a solid grasp on simple definitions of category theory up to natural transformations

John Baez (Jun 26 2020 at 18:48):

has some of the definitions you need to know concerning monoidal categories. But you probably want something more expository too. Maybe some folks can suggest their favorite intros to monoidal categories.

Evan Patterson (Jun 26 2020 at 18:54):

Yeah, what I wrote in that chapter is not a substitute for a proper introduction to monoidal categories. I first learned about monoidal categories from the early chapters of New Structure for Physics, particularly the Rosetta Stone paper and Categories for the practicing physicist (much of which doesn't require that you know anything about physics). I like both these introductions a lot.

Javier Prieto (Jun 26 2020 at 19:10):

+1 to the Rosetta paper - I believe that's the first place I read about them. Chapters 2 and 4 of Seven Sketches may also be relevant.

Andrew Shulaev (Jun 26 2020 at 19:23):

Arthur Parzygnat (Jun 27 2020 at 14:51):

Is there a way to access today's meeting without signing up on the meetup? If it's a hassle, I can just sign up (I'm just being lazy and don't want to have to keep another password on record somewhere). Update: nevermind, a friend hooked me up with the info.

Oliver Shetler (Jun 27 2020 at 15:47):

Sure. Just go to the meeting link (it's publicly available) and take the zoom link / zoom ID. We'll use the same ID for all our meetings. No need to make a meetup account. It's just a conveient way for me to organize.

Oliver Shetler (Jun 27 2020 at 15:47):

Arthur Parzygnat (Jun 27 2020 at 15:54):

Actually, the Zoom ID is masked (and probably for a good reason). It states that only attendees can view the link. But I did obtain it from a friend who signed up.

Oliver Shetler (Jun 27 2020 at 15:59):

Fabrizio Genovese (Jun 27 2020 at 16:01):

I'll try to attend but that will be 7PM here, so I'll probably have to leave early

Oliver Shetler (Jun 27 2020 at 16:01):

Fabrizio Genovese (Jun 27 2020 at 16:01):

Oliver Shetler (Jun 27 2020 at 16:02):

impressive. would not have expected that. Here's the planned recurring meeting time and zoom ID

Oliver Shetler (Jun 27 2020 at 16:02):

Fabrizio Genovese (Jun 27 2020 at 16:58):

Joshua Meyers (Jun 27 2020 at 17:02):

Tomáš Gonda (Jun 27 2020 at 18:37):

By the way, if this reading group is going to take off (as it seems like it is), it would probably be a good idea to create its own stream (maybe learning:statistics?) for it. I don't think I have the privileges to move the existing threads to a new stream though, so a moderator would probably have to take care of that.

Oliver Shetler (Jun 27 2020 at 18:53):

I second that. It would be convenient for this to be it's own thread, so that we can create sub-threads, rather than creating separate threads for each purpose ("housekeeping", "scheduling", etc.)

John Baez (Jun 27 2020 at 21:24):

Oliver Shetler (Jun 28 2020 at 17:34):

It seems like machine representation of statistical models is a big source of interest for a lot of people. That's definitely a theme we should keep in mind as we read. If the interest remains strong, it will make sense to look at the machine representation portions of Patterson's paper as soon as we've developed the general foundations we need.

Oliver Shetler (Jun 28 2020 at 17:46):

Thank you for the reference, this is a great paper. In the conclusion, the author says that psychologists can _either_ narrow the scope of their claims to reflect the scope of their models or ignore the issue, perpetuating the problem.

It seems like categorical statistics could help play a role in developing a "third option" where psychologists who are willing to work hard could develop statistical models that do, in fact, reflect most of what they want to claim. This is a very exciting idea for me, because my main domain of scientific interest is in psychology and brain science.

Hopefully the solutions will be sufficiently general that they can be exported from Category Theory and used by people who don't know CT.

Evan Patterson (Jun 28 2020 at 22:41):

I agree Oliver, it's a really interesting and enjoyable paper. I found it through Gelman's blog, where there is some commentary.

I also agree that we should be looking at options besides giving up on generalizability in the social sciences or simply ignoring the problem. Yarkoni points out the glaring disconnect between the general, verbal description of a theory and the specific, quantitative statistical model associated with a single experimental design. At the technical level, he suggests that multilevel modeling is helpful and that seems right. But for some reason, he never discusses what seems to me the obvious place to start: getting clear about what the verbal "theories" really mean. I'm not a psychologist by any stretch of imagination, but ideas like "ego depletion," "verbal overshadowing," etc strike me as being far too vague to constitute scientific theories in any meaningful sense. So, one possible path forward is to try to make mathematical sense out of psychological theories and how they are connected to specific statistical models and experimental designs. That seems like a problem that CT could help solve.

In general, I am deeply skeptical about the usefulness and reliability of scientific "theories" that do not go beyond verbal descriptions, and I think that scientists and statisticians need to get more serious about rigorizing this part of science. Right now, when I ask myself what is the right toolkit to solve that problem, I can't think of anything more likely than CT.

Oliver Shetler (Jun 28 2020 at 23:30):

I'm mostly in the same camp as you and old Karl Popper on that, though I'm quite optimistic about our ability to refine qualitative language to the point where it's sophisticated enough to call mathematical (yet still qualitative –– like "perfect sets" or "attracting spiral nodes" etc.)

One way forward might be to focus primarily on incorporating the ambiguity in these theories, rather than excoriating it (as many verificationists do).

For example, in the case of ego depletion, the overall idea is that (1) humans operate at different "rates" while in different motivational states (akin to temperature)* and (2) operating at different "temperatures" consume a virtual resource, which behaves like a conserved quantity in the short term, and behaves like a metabolic resource that replenishes in the medium term. We also know that this construct is virtual, and not valid, because there are counter examples.

For example, runners can get a second and third wind if they push past perceived exhaustion. More problematically, working on a project all day every day can be invigorating or exhausting depending on the psychological meaning of the situation to a person. However, even in this case, a person will eventually succumb to the need for sleep or distraction or both. Therefore, any refined theory will have to model semantic frames and get clearer about how to define the "temperature" of a person's motivational state (see * below for one possible refinement).

If I was earnestly working on this problem, my overall approach would be to start with a naive overly precise model –– a resource theory. Then I would generalize to a manifold of resource theories. First, I would pick a manageable domain for my theory (a specific sport, the military, academia, etc). I would do some phenomenological research to figure out which dimensions are appropriate to include in my model. That is, I would (1) reflect on the issue, (2) I would gather a maximally variable set of cases of interest and (3) do multidimensional scaling surveys where I ask people to say how similar the different situations I've collected are, thereby extracting the dimensionality of the principal components.

Next, I would generalize my theory to a manifold of dynamical descriptions. I would try to construct a qualitative transition diagram like the one Strogatz reproduces in his book Dynamical Systems and Chaois:
MK1aC.gif

but one that characterizes when people "give up" or change motivational states in other ways, with respect to the dimensions I constructed using multidimensional scaling. (Most likely, the model would be a dynamical system theory whose underlying quantities describe probabilities as well as aggregated states such as the "temperature" I described above, so it would be a highly layered model).

Then I would use statistically appropriate empirical data––and anecdotal counterexamples––to look for discrepancies between my qualitative model of when people give up and when they actually give up. Then I would repeat for another domain, and another until I could convince some poor grad student that s/he should take up my cause :smiling_devil:

Overall, by focusing on building a qualitative model of a class of "models," or a class of classes of "models," it's possible to build a model that is sufficiently ambiguous / qualitative to be true to the idea you are describing. It's a lot of work, which is why people rarely do it, but it's possible. At least, I have faith that it is possible in the same way that enlightenment natural philosophers such as Galileo had faith that the universe was 'rational.'

I couldn't agree more. In the above example, CT could make the process of making metaphors precise and extending models much more approachable than without CT.

My hope is that Category Theory can be a secret tool (then, hopefully, a not-so-secret tool) for making these kinds of problems tractable. (there are probably a lot of problems with my off-the-cuff 'proposal' but you get the idea)

[*] This is metaphor may be more literal than it seems. Georg Northoff has a theory of consciousness that quantitatively relates the phenomenology of mood to the variability of neural signals (as measured by EEG signals and fast magnetic imaging). Northoff identifies the prefrontal / orbitofrontal brain region as the source of perceptions about the outside world and he identifies the thalimaco-parietal region with perceptions about the inner world. These relations are relative. For example, a person who has high neural variability in the prefrontal region and low variability in the thalimaco-parietal region would feel as if the world is moving "too fast" for them, causing the mood of depression. People with the reverse condition feel manic, even though their thoughts are disordered. So the metaphor of mood or motivation as "temperature" has a stronger foundation than you'd think at first glance.

Bradley Saul (Jul 09 2020 at 00:08):

Evan - Thanks for sharing that paper. I'll just share that a related topic in causal inference is called "transportability", or to quote this paper: "transferring causal knowledge collected in several heterogeneous domains to a target domain in which only passive observations and limited experimental data can be collected".

Paolo Perrone (Jul 14 2020 at 19:47):

Mikael Vejdemo-Johansson (Aug 20 2020 at 17:14):

One potential direction we could add for future reading could be Baudot & Bennequin on statistical quantities through homological algebra.
https://www.youtube.com/watch?v=-KrPrjBUPyo
Baudot P, Bennequin D. The homological nature of entropy. Entropy. 2015 May;17(5):3253-318.
Basically, as I understand it (and I don't quite understand their work yet) - they create an abelian (?) category in which entropy and relative entropy appear as the essentially unique generators of non-trivial cohomology classes through the bar construction.

Peter Arndt (Aug 21 2020 at 13:53):

What a whirlwind talk! I would love to dig into this paper and also Vigneaux's thesis!

Peter Arndt (Aug 21 2020 at 13:54):

Arthur Parzygnat (Aug 22 2020 at 16:58):

Sorry ya'll. I won't be able to make today's meeting! Would it be possible if the next "HW" assignment is posted here for the following meeting? Thanks in advance!

Oliver Shetler (Aug 22 2020 at 18:03):

Hi all, we've decided that we've reached a point where everybody has a good foothold on the concepts from McCullagh. We've decided to move on to reading Patterson's thesis as a next step because he extends the ideas in McCullagh.

This week, we will be taking a first look at Evan Patterson's PhD Thesis "The Algebra and Machine Representation of Statistical Models" available here:
https://arxiv.org/pdf/2006.08945.pdf

Patterson extends the ideas from our last paper by McCullagh. Please read the introductory section and watch Patterson's presentation available here:
https://www.youtube.com/watch?v=Kzl2N9SH6H8

We will discuss reading goals and strategies at this session and decide what to do going forward.

Stream: deprecated: statistics reading group

Topic: general

Arthur Parzygnat (Jun 09 2020 at 09:59):