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The original was posted on /r/machinelearning by /u/Eamo853 on 2024-11-01 15:07:42+00:00.

To Clarify what I mean (also my background is more statistical but I’ve a problem with a quite nonlinear relationship)

Say I have inputs (predictor variables) for example: [x1,…,x10] which are all inherently numerical (ie no dummies) , and a continuous numerical output y, and say I fit some NN as y ~ x1 +… x10 (we can assume a relatively simple architecture, ie no CNN/RNNs )

If I then say was given [x2…x10,y] is there a way to predict what value of x1 is expected.

Some current thoughts I have, for a relatively simple statistical model which continuously maps the relationship between x1 and y with everything else fixed ( like a linear regression) this is trivial. From a neural network I’m guessing certain conditions would need to be made to the structure if this was to work, eg any activation functions would need to be themselves invertible.

I’m wondering are this something that is actively used or is there any research on this. Alternatively would a better option just be create two models

y = F(x1,…,x10) and x1 = G(x2,.,x10,y)

Thanks in advanced