# Learning a vector function [closed]

The goal is to learn a function $f$ of the form:

$f:\mathbb{R} \rightarrow \mathbb{R}^n$, $n \ge 1$

Are there machine learning techniques that can do it?

Thank you.

• Can you please tell us what you have tried? For example a ANN is generality regarded as a universal function approximator. Is this something like you are looking for? – usεr11852 says Reinstate Monic Dec 5 '15 at 7:17
• I have done some research and I think that the problem is of computing functions whose range is in a Hilbert space (paper). I have also found that multi-label classification might solve the problem. I am not sure which one is the best. – rmas Dec 5 '15 at 7:48
• What is $D$? What kind of data have you observed? – Juho Kokkala Dec 5 '15 at 8:27
• Let's say the observed data are of the form $(x, y_1,..., y_n)_i$, $i \in [1,m]$ – rmas Dec 5 '15 at 8:39

One simple, though not necessarily the most effective, way is to view it as $n$ regular univariate regression problems.
If you have sufficient data, it's particularly easy to phrase these problems as a neural network; just have multiple outputs at the end of your architecture, and use e.g. $L_2$ loss.