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Joined 4 years ago
Joined 4 years ago
I agree that, computationally, it is hard to justify the use of Bayesian methods on large-scale neural networks when stochastic gradient descent (and friends) is so damn efficient and effective.
On the other hand, the fact that there's a dependence on (subjective) priors is hardly a fair critique: non-Bayesian training of neural networks also depends on the use of (subjective) loss functions with (subjective) regularization terms (in fact, it can be shown that, mathematically, the use of priors is precisely equivalent to adding regularization to a loss function). Non-Bayesian training of neural networks is not "a failed approach" just because someone can arbitrarily choose L1 regularization (i.e., a Laplacian prior) over L2 regularization (i.e., a Gaussian prior).
Furthermore, we do have some intuition over NN parameters (particularly when inputs and outputs are properly scaled): a value of 10^15 should be less likely than a value of 0. Note that, in Bayesian practice, people often use weakly-informative priors (see, e.g., http://www.stat.columbia.edu/~gelman/presentations/weakprior...) to encode such intuitive statements while ensuring that (for all practical purposes) the data will effectively overwhelm the prior (again, this is equivalent to adding a minimal amount of regularization to a loss function, to make a problem well-posed when e.g. you have more parameters than data points).
So... unless I'm understanding something incorrectly, something like "the three last moves plus 17 bits of state" (plus the current board state) should be enough to treat chess as a memoryless process. Doesn't seem like too much to track.
Given that this issue applies to all proprietary/non-opensource software, which is the overwhelming majority of software out there, you can hardly blame GPL3 for this fact of life.
These days, base R already includes a native pipe operator (and it is literally `|>`, rather than magrittr's `%>%`).
More like "an effect this large, or larger, should happen by chance 1 time out of 20 in the hypothetical universe where we already know that the true size of the effect is zero".
Part of the problem of p-values is that most people can't even parse what it means (not saying it's your case). P-values are never a statement about probabilities in the real world, but always a statement about probabilities in a hypothetical world where we all effects are zero.
"Effect sizes", on the other hand, are more directly meaningful and more likely to be correctly interpreted by people on general, particularly if they have the relevant domain knowledge.
(Otherwise, I 100% agree with the rest of your comment.)
A p-value does not measure "importance" (or relevance), and its meaning is not dependent on the research field or domain knowledge: it mostly just depends on effect size and number of replicates (and, in this case, due to the need to apply multiple comparison correction for effective FDR control, it depends on the number of things you are testing).
If you take any fixed effect size (no matter how small/non-important or large/important, as long as it is nonzero), you can make the p-value be arbitrarily small by just taking a sufficiently high number of samples (i.e., replicates). Thus, the p-value does not measure effect importance, it (roughly) measures whether you have enough information to be able to confidently claim that the effect is not exactly zero.
Example: you have a drug that reduces people's body weight by 0.00001% (clearly, an irrelevant/non-important effect, according to my domain knowledge of "people's expectations when they take a weight loss drug"); still, if you collect enough samples (i.e., take the weight of enough people who took the drug and of people who took a placebo, before and after), you can get a p-value as low as you want (0.05, 0.01, 0.001, etc.), mathematically speaking (i.e., as long as you can take an arbitrarily high number of samples). Thus, the p-value clearly can't be measuring the importance of the effect, if you can make it arbitrarily low by just having more measurements (assuming a fixed effect size/importance).
What is research field (or domain knowledge) dependent is the "relevance" of the effect (i.e., the effect size), which is what people should be focusing on anyway ("how big is the effect and how certain am I about its scale?"), rather than p-values (a statement about a hypothetical universe in which we assume the null to be true).
Perhaps, but this is not something unique to KANs: any symbolic regression method can (at least in theory) find such simple expressions. Here is an example of such type of work (using non-KAN neural networks): https://www.science.org/doi/10.1126/sciadv.aay2631
Rephrasing: just because you can reach simple expressions with symbolic regression methods based on neural networks (or KANs) does not necessarily imply that neural networks (or KANs) are inherently interpretable (particularly once you start stacking multiple layers).
I'm not sure this changes if you look at a cepstral representation (as suggested in the article). In this case, the DC component represents the (white) noise level in the raw audio space (i.e., the spectrum averaged over all frequencies), so it doesn't have strong semantics either (other than... "how noisy is the waveform?").
I mean that "trying to argue based on (your perception of) the person you are talking to, rather than what is being discussed, is a bad argumentation strategy".
> How is this specific decision, or some of the other examples/laws you've mentioned not authoritarian at least to some extent?
Even if it is (which you surely haven't demonstrated), in what way does that imply that I (or anyone else) feel "appeal towards authoritarianism"? Stick to discussing the subject, instead of discussing the people you are talking to, if you want to be taken seriously.
> It doesn't mean that they are not necessarily or unjustifiable in every single case.
If they are legally, morally and ethically justifiable (at least sometimes), then it's not really "authoritarianism": it's just "rule-of-law".
> I kept repeating this point in every comment I made. Yet you ignored it from the very beginning.
No. The only time you mentioned it (in a response to me) was when I called you out. If you disagree, please post the supposed previous comment you made (in response to me) where you bring up the VPN ban issue.
> Also it's not a different subject, it's intrinsically related to the decision made to ban Twitter since that's how the judge decided to enforce it.
From what I understand, the only thing that was banned was the use of circumvention technologies for the purpose of accessing Twitter (which seems legitimate if his previous ruling is to be effectively enforced). From what I understand, the blanket ban of VPN technologies (which does not seem legitimate to me) has been reversed.
> The point that different countries have different laws? Well that's a fact, not sure how can I address it.
The way to address it is to accept that US laws (and US standards of free speech) do not apply to this case, since it is outside of US jurisdiction. Furthermore, to accept that, if a company wants to operate in a certain country, it kind of has to abide by its laws and regulations (regardless of whether they are legitimate or not).
> However I'm curious where do you draw the line? e.g. the USSR had laws, Russia has laws, Venezuela has laws so does China, Hungary and every other country. They all have vary different attitudes to freedom of speech and a bunch of other matters, do you believe that they are all equally valid, reasonable and legitimate?
Obviously not, but the fact remains: if you want to operate in USSR, Russia, Venezuela, China, Hungary, or wherever, you need to comply with local regulations and laws. Or, of course, you can choose not to, but then it is quite likely that local authorities will do whatever they can to prevent your company from operating in their country.
Musk/Twitter has no problem complying with Turkish and Indian court requests and laws, even when it involves censorship. Yet, it can't seem to do the same when it comes to Brazilian court requests and laws. Strange...
In this particular case, I do not have enough information to state with certainty whether I think this particular case is legitimate or not, but it does seem to be lawful (which is the criterion that is seemingly important for Twitter/Musk).
I have no particular preference with regards to whether Musk chooses to be consistent or not: that's his decision and he/Twitter is the one that has to endure the consequences of his actions (not me). Since I am not a Twitter user, it does not affect me either way, and I don't see how it will significantly affect Brazilian's capacity to freely communicate (note: there are plenty of other private communication platforms that do comply with Brazilian law... Telegram, Whatsapp, Instagram, Facebook, etc.).
On the other hand, I do think it is hypocritical to claim to be a "defender of free speech", and then both engage in non-state-mandated censorship AND comply with state-mandated censorship (as long as it suits him or Twitter). It's a laughable claim. That was my only point.
I don't know if, in this case, it is justified or not, but it seems to be lawful (the same way that the censorship requests in India and Turkey were), as far as I can tell (I assume a judge of the Supreme Court knows a bit more about Brazilian law than you and me).
Given that Musk/Twitter seemingly has no problem complying with lawful censorship demands (or engaging in arbitrary censorship even without lawful censorship demands), it seems clear to me that Musk has no problem with "more censorship in the world". That was my only point.
My personal opinion on whether there is higher or lower need for censorship in the world is rather irrelevant (since I have no power or platforms to censor), but I certainly see no problem in actively censoring terrorists, bots, spammers and scammers (for example).
I'd argue the choice is still subjective, since you are still only testing over a limited (subjective) set of options. If you are doing this properly (i.e., using an independent validation set), then you can apply the same approach to a Bayesian method and obtain the same type of information ("when I use prior A vs. prior B, how does that change the generalization/out-of-bag error properties of my model?"), without violating any properties or theoretical guarantees of "Bayesianism".
> A Bayesian could try the same thing: try out several priors, and pick the one that performs best in validation. But if you pick your prior based on the data, then the classic theory about “principled quantification of uncertainty” doesn’t apply any more.
If you subjectively define a set of possible priors (i.e., distributions and parameters) to test in a validation setting, then you are not picking your prior based on the data (again, assuming that you have set up a leakage-free partition of your data in training and validation data), and you are not doing empirical Bayes, so you are not violating any supposed "principled quantification of uncertainty" (if you believe that applying a standard subjective Bayesian approach provides you with "principled quantification of uncertainty").
My point was that, in practice, there are ways of choosing (subjective) priors such that they provide sufficient regularization while ensuring that their impact on the results is minimized, particularly when you can assume certain things about the scale of data (and, in the context of neural networks, you often can, due to things like "normalization layers" and prior scaling of inputs and outputs): "subjective" doesn't have to mean "arbitrary".
> So you’re left using a computationally unwieldy procedure that doesn’t offer theoretical guarantees.
I won't argue about the fact that training NN using Bayesian approaches is computationally unwieldy. I just don't see how evaluating a modelling decision (be in Bayesian or non-Bayesian modelling), using a proper validation process, would violate any specific theoretical guarantees.
If you can explain to me how evaluating the generalization properties of a Bayesian training recipe on an independent dataset violates any specific theoretical guarantees, I would be thankful (note: as far as I am concerned, "principled quantification of uncertainty" is not a specific theoretical guarantee).