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it's still an extremely valuable tool. just as we see in mathematics, closed forms (and short and elegant proofs) are much coveted luxury items. for many basic

by pas 2y ago

it's still an extremely valuable tool. just as we see in mathematics, closed forms (and short and elegant proofs) are much coveted luxury items. for many basic/fundamental mathematical objects we don't (yet) have simple mechanistic ways to compute them. so if a probabilistic model spits out something very useful, we can slap a nice label on it and call it a day. that's how engineering works anyway. and then hopefully someday someone will be able to derive that result from "first principles" .. maybe it'll be even more funky/crazy/interesting ... just like mathematics arguably became more exciting by the fact that someone noticed that many things are not provable/constructable without an explicit Axiom of Choice. https://en.wikipedia.org/wiki/Nonelementary_integral#Examples https://en.wikipedia.org/wiki/Nonelementary_integral#Example...

thfuran 2y ago
>closed forms (and short and elegant proofs) are much coveted luxury items. Yes, but we're taking about roughly the opposite of a proof
- pas 2y ago
  but in usual natural sciences we don't have proofs, only data and models, and then we do model selection (and through careful experiments we end up with confidence intervals) and it seems with these molecular biology problems we constantly have the problem of specificity (model prediction quality) vs sensitivity (model applicability), right? but due to information theory constraints there's also a dimension along model size/complexity. so if a ML model can push the ROC curve toward the magic left-up corner then likely it's getting more and more complex. and at one point we simply are left with models that are completely parametrized by data and there's virtually zero (direct) influence of the first principles. (I mean that at one point as we get more data even to do model selection we can't use "first principles" because what we know through that is already incorporated into previous versions of the models. Ie. the information we gained from those principles we already used to make decisions in earlier iterations.) Of course then in theory we can do model distillation, and if there's some hidden small/elegant theory we can probably find it. (Which would be like a proof through contradiction, because it would mean that we found model with the same predictive power but with smaller complexity than expected.) // NB: it's 01:30 here, but independent of ignorance-o-clock ... it's quite possible I'm totally wrong about this, happy to read any criticism/replies
deleted 2y ago
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by pas 2y ago

thfuran 2y ago

>closed forms (and short and elegant proofs) are much coveted luxury items. Yes, but we're taking about roughly the opposite of a proof

pas 2y ago
but in usual natural sciences we don't have proofs, only data and models, and then we do model selection (and through careful experiments we end up with confidence intervals) and it seems with these molecular biology problems we constantly have the problem of specificity (model prediction quality) vs sensitivity (model applicability), right? but due to information theory constraints there's also a dimension along model size/complexity. so if a ML model can push the ROC curve toward the magic left-up corner then likely it's getting more and more complex. and at one point we simply are left with models that are completely parametrized by data and there's virtually zero (direct) influence of the first principles. (I mean that at one point as we get more data even to do model selection we can't use "first principles" because what we know through that is already incorporated into previous versions of the models. Ie. the information we gained from those principles we already used to make decisions in earlier iterations.) Of course then in theory we can do model distillation, and if there's some hidden small/elegant theory we can probably find it. (Which would be like a proof through contradiction, because it would mean that we found model with the same predictive power but with smaller complexity than expected.) // NB: it's 01:30 here, but independent of ignorance-o-clock ... it's quite possible I'm totally wrong about this, happy to read any criticism/replies

deleted 2y ago

[deleted]