Bayesian here. I'll lay down my thoughts after reading this post in no particular order, I'm not trying to construct a coherent argument pro/against the argument of your post, not due to lack of interest but due to lack of time, though in general it'll be evident I'm generally pro-Bayes:
- I have the impression that Yudkowsky has lowered his level of dogmaticism since then, as is common with aging. I've never read this explicitly discussed by him, but I'll cite one holistic piece of my evidence: that I've learned more about the limitations of Bayes from LessWrong and MIRI than from discussions with frequentists (I mean, people preferring or mostly using frequentist stuff or at least feeling about Bayes like a weird thing, not that they would be ideologues and not use it). Going beyond Bayes seems like a central theme in Yudkowsky's work, though it's always framed as extending Bayes. So I'll take a stab at guessing what Yudkowsky thinks right now about this, and it would be that AIXI is the simplest complete idealized model of Bayesian agent, it's of course a model and not reality, and general out-of-formal-math evidence aggregation points to Bayes being substantially an important property of intelligence, agency, knowledge that's going to stick around like Newton is still used after Einsten, and this amounts to saying that Bayes is a law, though he wouldn't today describe it with the biblical vibes he had when writing the sequences.
- I empirically observed Bayes is a good guide to finding good statistical models, and I venture that if you think otherwise you are not good enough at the craft. It took me years of usage and study to use it myself in that sense, rather than just using Bayesian stuff as pre-packaged tools and basically equivalent to other frequentist stuff if not for idiosyncratic differences in convenience in each given problem.
- I generally have the impression that the mathematical arguments you mention focus a lot on the details and miss the big picture. I don't mean that they are wrong; I trust that they are right. But the overall picture I'd draw out of them is that Bayes is the right intuition, it's substantially correct, though it's a simplified model of course and you can refine it in multiple directions.
- Formally, frequentist estimators are just any function. Though of course you'll require sensible properties out of your estimators, there's no real rule about what a good frequentist estimator should be. You can ask it to be unbiased, or to minimize MSE, under i.i.d. repetition. What's if i.i.d. repetition is not a reasonable assumption? What if unbiased is in contradiction with minimizing MSE? Bayes gives you a much much smaller subset of stuff to pick from in a given problem, though still large in absolute terms. That's the strength of the method; that you should not in practice need anything else out of that much smaller subset of potential solutions for your practical inference problems. They are also valid as frequentist solutions, but this does not mean that Bayes is equivalent to frequentist, because the latter does not select so specifically those solutions.
- OLS is basically Bayesian. If you don't like the improper prior, pick a proper very diffuse one. This should not matter in practice. If it happens to matter in some case, I bet the setup is artificial and contrived. OLS is not a general model of agency and intelligence, it's amongst the simplest regression models, and it need not work under extreme hypothetical scenarios, it needs to work for simple stuff. If I ran OLS and got beta_1 = 1'000'000'000'000, I would immediately think "I fucked up", unless I was already well aware of putting wackily unscaled values into the procedure, so a wide proper prior matches practical reasoning at an intuitive level. Which does not mean that Bayes is a good overall model of my practical reasoning at that point, which should point to "re-check the data and code", but I take it as a good sign for Bayes that it points in the right direction within the allowance of such a simplified model.
- Thank you for the many pointers to the literature on this, this is the kind of post one gets back to in the future (even if you consider it a rush job).
In the last few years, as I read stuff about AI US vs. China in the blogosphere, I've always felt confused by this kind of question (exports to China or not? China this or that?). I really don't have an intuition of what's the right answer here. I've never thought about this deeply, so I'll take the occasion to write down some thoughts.
Conditional on the scenario where dangerous AI/point of no return comes in 2035, if AI development continues to be free, so not because say it would come earlier but was regulated away:
Considering the question Q = "Is China at the edge with chips in 2035?":
Then I consider three policies and write down P(Q|do(Policy)):
P(Q|free chips trade with China) = 30%
P(Q|restrictions on exports to China of most powerful chips) = 50%
P(Q|block all chips exports to China) = 80%
I totally made up these percentages; I guess my brain simply generated three ~evenly-spaced numbers in (0, 100).
Then the next question would be: what difference does Q make? Does it make a difference if China is at the same level of the US?
The US is totally able to create the problem in the first place from scratch in a unipolar world. Would an actually multipolar world be even worse? Or would it not make any difference, because the US is self-racing? Or would it have the opposite effect, where the US is forced to actually sit at a table?
I'm jumping to reply here having read the post in the past and without re-reading the post and the discussion, so maybe I'll be redundant. With that said:
I think that nonparametric probabilistic programming will in general have the same order of number of parameters as DL. The number of parameters can be substantially lower only when you have a neat simplified model, either because
1. you understand the process to the point of constraining it so much, for example in physics experiments
2. it's hopeless to extract more information than that, in other words it's noisy data, so a simple model suffices
1Last time I was in the US, I often relied on the following pasta recipe to prepare multiple meals at once:
- fettuccine
- cook bacon in a pot with just a drip of olive oil (no other additions)
- cook pre-sliced mushrooms in another pot (no other additions)
- throw everything into the drained fettuccine in a pot
- add a few cheese singles and mix everything until they are melt and blended
The thing about this recipe is that I've observed it keeps the original flavor if kept in the fridge and re-heated in the microwave, I kept it in the fridge up to 10 days. Many other pasta sauces alter their flavor in a bad way if so processed, and freezing was even worse in my experience.
Yeah I had complaints when I was taught that formula as well!
Reasons I deem more likely:
1. Selection effect: if it's unfeasible you don't work on it/don't hear about it, in my personal experience n^3 is already slow
2. If in n^k k is high, probably you have some representation where k is a parameter and so you say it's exponential in k, not that it's polinomial
I don't like the notation because appears as a free RV but actually it's averaged over. I think it would be better to write .
While reading this, I thought "Man, an autistic by default is going to ram through all this social mechanism like a train".
I will never get the python love they also express here, or the hate for OOP. I really wish we weren’t so foolish as to build the AI future on python, but here we are.
I'm confused. How can they "hate OOP" (which I assume stands for "Object Oriented Programming") and also love Python, which is the definitive everything-is-an-object, everything-happens-at-runtime language? If they were ML professionals I'd think it was a rant about JAX vs Pytorch, but they aren't right?
EDIT: it was pointed out to me that e.g. Java is more OOP than Python, and objects do not count as Objects if you don't have to deal with classes & co yourself but just use them in a simple fashion. Still, love Python & hate OOP? In this context they are probably referring to Pytorch, that I would call OOP for sure, it does a lot of object-oriented shenanigans.
A general way my mental model of how statistics works disagrees with what you write here is on whether the specific properties that are in different contexts required of estimators (calibration, unbiasedness, minimum variance, etc.) are the things we want. I think of them as proxies, and I think Goodhart's law applies: when you try to get the best estimator in one of these senses, you "pull the cover" and break some other property that you would actually care about on reflection but are not aware of.
(Not answering many points in your comment to cut it short, I prioritized this one.)