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Machine learning leads mathematicians to unsolvable problem

nature.com

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Re: Machine learning leads mathematicians to unsolvable problem

#11

Post by Eridrus »

byebyetech wrote: post #4
verroq wrote: post #3

Earlier quoted context omitted.

The ML field today is all about results. Get the high scores and figure out the math later. Not that there is anything wrong with this, we still at the stage where we're banging rocks together wondering what works and what doesn't, and the theories will come later.

So what is the meaning of "ML experts" if all they do is trial and loss experiments! Is Math PhD just used for hiring signal rather than actual requirements to do ML projects?

Yes, there is no need to have a PhD to do ML, either applied or research. Not to say there isn't good research using advanced mathematical/statistical methods, but most of it is not. It's entirely a signaling game.

Re: Machine learning leads mathematicians to unsolvable problem

#13

Post by SatvikBeri »

min2bro wrote: post #2

Where is mathematics in ML today? Most of that are happening under the hood and all algorithms are just a black box.

It's all around. The math portion just doesn't get as much hype.

For example, Goodfellow and Bengio's book on Deep Learning talks a lot about connections to Bayesian Inference, Classical Statistics, Information Theory, and a bit about Topology.

Christopher Oolah's blog gives plenty of great explanations of mathematical topics.

Personally, I use Math in my work all the time. Thinking in terms of Information Theory has let me quantify and compare algorithms that seemed difficult to evaluate at first. And several times, I've seen a business make the wrong decision due to lack of Math/Stats background.

I don't mean to be a Math snob – you can absolutely do a lot of valuable work treating algorithms as black boxes. But the Math is there, and it is being used.

Re: Machine learning leads mathematicians to unsolvable problem

#14

Post by repiret »

perfmode wrote: post #6
thyrsus wrote: post #5

I don't understand how a result concerning infinities can apply to a finite number of data points represented by finite (bounded - probably by 2^32) integers processed in finite time.

The reals are infinite. Float/double So, while I think your question is interesting and good, I don’t think integer size is a strong counterexample in support of a different conclusion.

float/double can store a subset of the rationals plus some other values which aren’t found in the reals

Re: Machine learning leads mathematicians to unsolvable problem

#15

Post by mensetmanusman »

byebyetech wrote: post #4
verroq wrote: post #3

Earlier quoted context omitted.

The ML field today is all about results. Get the high scores and figure out the math later. Not that there is anything wrong with this, we still at the stage where we're banging rocks together wondering what works and what doesn't, and the theories will come later.

So what is the meaning of "ML experts" if all they do is trial and loss experiments! Is Math PhD just used for hiring signal rather than actual requirements to do ML projects?

It’s an exciting time because the field is getting to the point where ‘complexity is unbounded’

I.e. in many materials or chemistry fields where you start operating with over 100 variables, you begin to develop a dark arts of understanding because what is being attempted is beyond the ability of computers to model.

You can do chemistry without a PhD, but your ability to systematically try to address the complexity may be hindered without the training. Likewise with ‘ML experts’ (I hope they get a cool word some day to describe their profession).

Re: Machine learning leads mathematicians to unsolvable problem

#16

Post by shoo »

thyrsus wrote: post #5

I don't understand how a result concerning infinities can apply to a finite number of data points represented by finite (bounded - probably by 2^32) integers processed in finite time.

i think you're alluding to an interesting question: in what cases does this "undecidability of learnability" result apply?

the paper seems to talk about binary classifiers `h : X --> {0, 1}`, where each classifier h belongs to some family `F` of functions subseteq `{h : X --> {0, 1}}`, and where observed samples are drawn from some unknown distribution P over X.

so, it probably depends upon the choice of `X` and `F`, but i dont have enough of a handle on the theory to understand this.

Re: Machine learning leads mathematicians to unsolvable problem

#18

Post by fucking_tragedy »

p1esk wrote: post #17

This work was published in “Nature Machine Intelligence“, the journal boycotted by pretty much everyone who matters in ML. Reflects poorly on the authors, regardless of the actual merits of their finding.

As someone who isn't in the know, I found this[1] Forbes article about the journal. Forbes portrays the opposition as opposing the fact that it's a closed access journal, but are there other points of contention that weren't reported in the article?

[1] https://www.forbes.com/sites/samshead/2018/04/30/tech-giant-...

Re: Machine learning leads mathematicians to unsolvable problem

#19

Post by joe_the_user »

p1esk wrote: post #17

This work was published in “Nature Machine Intelligence“, the journal boycotted by pretty much everyone who matters in ML. Reflects poorly on the authors, regardless of the actual merits of their finding.

As far as I can tell, the article isn't really of any interest either.

Formulating a proposition that is independent of standard axioms is simple. Formulating it in the language of machine learn is an exercise. The main thing is the authors didn't provide any motivation for this to matter to the overall enterprise of machine learning, because there isn't motivation for this. It's just a novelty.

Re: Machine learning leads mathematicians to unsolvable problem

#20

Post by sologoub »

p1esk wrote: post #17

This work was published in “Nature Machine Intelligence“, the journal boycotted by pretty much everyone who matters in ML. Reflects poorly on the authors, regardless of the actual merits of their finding.

Had to lookup what the boycott was about - free access and fees: http://www.sciencemag.org/news/2018/05/why-are-ai-researcher...
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