I have some inputs and outputs of a set of functions, and I want to be able to find/approximate any given input vector from its corresponding output vector (In other words learn the inverses of these functions without knowing the form of the function explicitly). What sort of machine learning techniques would work well for this? Naively I am leaning toward neural networks, since that is what I have the most familiarity with, but I am curious what other options there are for these sorts of mathematical approximations.
2
-
$\begingroup$ Just to note that the problem in its general form is unsolvable: take the function f(x)=3, there's an infinite number of possible inputs x for a single y=3. So the question is actually equivalent to "can any function be approximated?" once the constraints on the existence of an inverse function are satisfied. Beyond this point I'm not competent, but this answer is also interesting. $\endgroup$– ErwanCommented Jun 16, 2022 at 21:30
-
$\begingroup$ Thank you for pointing this out! The hope would be that because I am using a vector of multiple inputs/outputs from different functions, that this would offset any one function taking the same value at multiple places (More broadly part of the goal for the project is to identify such a 'basis' of functions/outputs from the input space such that we know each output vector is unique). I can also confirm that the outputs as a whole do depend on the inputs in my specific case, i.e. I don't believe there's any function I am using which is completely independent of the input like y=3 would be. $\endgroup$– nighthawkCommented Jun 20, 2022 at 17:08
Add a comment
|