Unsupervised Learning

by rrusczyk, Jun 26, 2009, 1:48 AM

An AoPS parent just sent me this article on "unsupervised learning".

One key excerpt struck home:
Quote:
But in unsupervised learning the student is given, say, the complete set of multiplication exams for the last 20 years--some problems with the right answers, some with the wrong ones--and it is up to the student to make sense of it all.

This is how I used math contest to train myself to solve problems. It's a fantastic way to learn, but only if you have good data to learn from. The trouble is, we humans can't process all available data, or even much of it, the way computers can. We humans need an effective filter to present the unsupervised learner with the best set of data to learn from. That's what math contests did for me, and what we're trying to do with AoPS now. (It also might be a future of Alcumus...)

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The article also brings up a fun linguistics problem for computer scientists-- unsupervised translation (and, I might add, part of speech tagging).

by Osud, Jun 26, 2009, 2:02 AM

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I think there's a major difference between training with contest problems and training with huge data sets like the article talks about. You're doing fundamentally different training: one for humans who can think creatively, and one for computers that perform tasks routinely, whether or not those tasks are routine for humans. It's not that you got problems and a bunch of answers/solutions, but only some were correct, nor that you had to figure out which axioms of arithmetic you were allowed to use. The terminology might be the same, but it means something entirely different, in my opinion.

Oh, and what the 'best data set to learn from' is very subjective. First we'd have to answer what the best results would be. Success on the SAT? AMC? USAMO? Mandelbrot? MATHCOUNTS? Good math researcher? And something as broad as Alcumus can't hope to serve everyone's needs in a completely unsupervised way, since there's no way to measure how much someone is learning outside of the problems you already have.

by SamE, Jun 26, 2009, 7:24 AM

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I guess I'm saying that my training for math contests trained me for almost everything I have done since: trading bonds, building AoPS, building a chicken coop...

The target is "what you want to do, whatever that may be", not "win a math contest" or "ace the SAT". I think a problem solving approach to learning math does this very well.

by rrusczyk, Jun 26, 2009, 3:31 PM

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"Make sense of it all?" Sounds like MIT Mystery Hunt style challenges, where directions are virtually never given, would teach this kind of skill fairly well.

by MellowMelon, Jun 27, 2009, 1:01 AM

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I'd be curious what our linguists and mathematicians would make of the following question:

In what year (if ever) will a computer successfully read and make a perfect score on the AMC 8, AMC 10-12, AIME, USAMO?

Is the act of writing a USAMO proof beyond the limits of any AI?

by djcordeiro, Jun 29, 2009, 1:38 PM

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