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I have feature data $X$ and four predictions $ (u_1, u_2, u_3, u_4) = f(X)$ with $u_1, u_2, u_3, u_4 \in \mathbb{R^+}$. $f$ is an unknown function (no assumptions on its properties) that needs to be learned to predict $u$ out of sample.

I have training data that consists of approx. 10k observations (rows) of $X$ and $f(X)$. A data-related problem is that I know that in my out-of-sample data I will observe many unseen feature values of two features $x_1$ and $x_2$ that I know to be quite important to the value of $f(X)$.

Is there a model that is well suited to learn a function $f$ and make multiple real-valued predictions $ (u_1, u_2, u_3, u_4) $, ideally such that $f$ also generalizes well to unseen data?

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    $\begingroup$ The description is of a regression model. Is there something else more complicated in the question? $\endgroup$
    – Craig
    Jul 28 at 15:32
  • $\begingroup$ I am re-reading the question. Is this a multi-output regression model? Instead of 1 output there are 4 for every row of input? $\endgroup$
    – Craig
    Jul 28 at 15:58
  • $\begingroup$ @Craig Thanks! Yes, you are right its actually more simple than I realized myself. Deep Learning for Multi-Output Regression should do the trick. I was coming from a more complicated problem formulation, writing out the questions actually helped. $\endgroup$
    – Mike Lang
    Jul 29 at 6:46
  • $\begingroup$ Glad I could help. There are a few ways to handle multi-output but it seems like you have a handle on one way. Writing or talking out the problem at hand often helps. $\endgroup$
    – Craig
    Jul 29 at 12:42

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Well, I am quite new on DS too, but I believe you will need to try some models to identify each one better fit on our data. Something like:

  1. Prepare the data (normalized or standardized).
  2. Split the data.
  3. Train the model.
  4. Validate.
  5. Tune.
  6. Use.

The model purpose is generalize the real world, so, you need to investigate if this unseen values is very far form the data that you have. This may lead you into a non-realist model and you need to collect more data.

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