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Is it possible to fit a NN given pairs (X, Y), such that NN(X) = Y using maximum-likelihood (ML) and not gradient descent (GD)?

Example:

  • I have a NN with weights W
  • I feed it with 10 samples X and get 10 output Y
  • I add noise e and get new output Y+e
  • I evaluate Y+e and assign them some weights
  • How do I perform a weighted fitting of pairs (X, Y+e)?

I was thinking about ML because I don't think that I can weigh the samples with GD. And I know that I could use ML if I would have, for instance, a Gaussian (or apply expectation-maximization to a mixture model).

I tried to search on Google but I did not find much. Any reference (and possibly some implementation) would be much appreciated.

Simon
  • 191
  • I think you have a regression problem. We commonly use neural networks for classification but we can also use them for regression. For pairs (X,Y) Y can be a target for an input of X. – Hugh Feb 18 '17 at 15:28
  • Could you plase examplify the scenario where you don't have the target (function)? In my opinion you can always find one if you map the linear predictor to the response. Even if the link funciton is the ulity function the target is the MSE. – Lerner Zhang Feb 18 '17 at 15:33
  • Thanks to the both of you. I have modified my question, since I did not state my problem clearly. – Simon Feb 18 '17 at 15:42

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