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Machine Learning: How does machine learning solve inverse mapping problem?

  • If an algorithm can learning the mapping from x to y, e.g. y=f(x), can ML learn the inverse mapping from from y to x? For example, the mapping from y to x1, x2... where, f(x1)=f(x2)=y. Can ML learn g(y) = x1 and g(y) = x2? Normally, the ML would probably generalize the pairs that, g(y) = (x1+x2)/2. Is it a good way to solve that?

  • Answer:

    In the typical machine learning problem, xxx is a vector with a bunch of entries, and yyy is either zero or one.  That gives you one covariate with two values and a bunch of labels for your training data, and that's not something that you're going to do well with. If you're trying to learn an invertible function, then you can make this work.  But that's a very special case, and not relevant for most problems.

Justin Rising at Quora Visit the source

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Machine Learning is exactly about solving inverse problems!  Thats the essence of the old thing.  See this old paper by Smale: http://www.ams.org/notices/200305/fea-smale.pdf the master lays it out I will comment..what we think of as machine learning (ala SVMs) is about solving Linear Integral Equations of the first kind http://charlesmartin14.wordpress.com/2012/09/28/kernels-greens-functions-and-resolvent-operators/

Charles H Martin

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