The objective is to build a classifier that produces M correct outputs when given N inputs.
Let a "sample" be M outputs and N inputs. Each output is some function some of the N inputs but the functions are not given. You only know that some of the N inputs can possibly combine to produce each of the M outputs.
Several samples are available for the machine learning algorithm to learn from, and in each sample, the functions for each output produced from what input sets are the exactly same.
It sounds like supervised learning but it doesn't seem to match exactly.
I'll provide an example:
Inputs: people = 6; salary = 100
outputs: width = 600; height = 100
Inputs: people = 3; salary = 60
outputs: width = 180; height = 60
Inputs: people = 5; salary = 101
outputs: width = 505; height = 101
The correct functions are then: width = people * salary; height = salary