Ratio of inputs to outputs

[PatWalters]

This is more of a philosophical question. I have a dataset with 5 inputs and 8 outputs (mostly quantities of impurities). I don't have much experience with multi-objective GP. Is there a rule of thumb for the ratio of the number of inputs to the number of outputs?

[AdrianSosic]

Hi @PatWalters, please apologize the late answer. Little time for philosophy at the moment 😄 I haven't seen any such rule so far and I doubt that one exists because it's probably impossible to quantify this in a general way. To me, this is a bit like the question "how many data points do I need to train a machine learning model" – it depends entirely on the context. Also, I think it depends on the specific aspect being asked and the structure of the model. For example, if your N -> M multi-objective GP (with N being input dimensions and M being output dimension) really is just a collection of M single-objective GPs of type N -> 1, then for each individual fit the number of output dimensions is completely irrelevant. In this case, the question is probably rather "for large M, can these individual GPs still lead to a coherent multi-objective decision"?

So my modest answer is: I honestly don't know 😬 Perhaps there are some theoretical results on this topic but at least I haven't seen anything like that.

[PatWalters]

@AdrianSosic, thanks for sharing your experience and releasing such a great package.