Machine learning leads mathematicians to unsolvable problem
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Re: Machine learning leads mathematicians to unsolvable problem
#2Where is mathematics in ML today? Most of that are happening under the hood and all algorithms are just a black box.
Re: Machine learning leads mathematicians to unsolvable problem
#3Where is mathematics in ML today? Most of that are happening under the hood and all algorithms are just a black box.
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.
Re: Machine learning leads mathematicians to unsolvable problem
#4Where is mathematics in ML today? Most of that are happening under the hood and all algorithms are just a black box.
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?
Re: Machine learning leads mathematicians to unsolvable problem
#5I 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.
Re: Machine learning leads mathematicians to unsolvable problem
#6I 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.
Re: Machine learning leads mathematicians to unsolvable problem
#7Where is mathematics in ML today? Most of that are happening under the hood and all algorithms are just a black box.
There's a very neat and often forgotten piece of math in learning, VC dimension (unrelated to venture capital):
https://en.m.wikipedia.org/wiki/Vapnik–Chervonenkis_dimensio...
Also, the reason why black box methods are such a big deal now is precisely because controlled/engineered methods turned out to be inferior (obvious example: image recognition; look no further than into the story of the dropout method and Alex Krizhevsky).
Edit: s/basically forgotten/often forgotten/ in the first sentence.
Re: Machine learning leads mathematicians to unsolvable problem
#8I 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.
Can you elaborate on this? Specifically, why isn’t integer size a good counterexample?
Re: Machine learning leads mathematicians to unsolvable problem
#9Where is mathematics in ML today? Most of that are happening under the hood and all algorithms are just a black box.
There's a very neat and often forgotten piece of math in learning, VC dimension (unrelated to venture capital): https://en.m.wikipedia.org/wiki/Vapnik–Chervonenkis_dimensio... Also, the reason why black box methods are such a big deal now is precisely because controlled/engineered methods turned out to be inferior (obvious example: image recognition; look no further than into the story of the dropout method and Alex…
It's not very forgotten if it's in the Learning from Data course, to say the least
Re: Machine learning leads mathematicians to unsolvable problem
#10I 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/doubles are finite. They only approximately model the real. And that's key. Because the fact that approximation works for a problem means it must be reasonably smooth, which means everything will be more well behaved and rules out the worst pathologies.