In Machine learning, we usually train models to predict X->Y. For example, a dataset with 20 input features X = (x0, x1, ... x19) and 3 output variables Y = (y0, y1, y2). The number of training/test data usually small, such as <1000 items or even <100 in the training set.
But in industry, the problem I have is that I want to know "how should I set X that I can get Y in a specific range or value"
Does anyone know how to solve this kind of "inverse prediction"? There are two ways in my mind:
The second method might be OK when the Y also have high dimensions. But usually, in my application, Y is very low-dimension and X is very high-dimension, which makes me think method 2 is not very practical.
Does anyone have any new thoughts? I think this should be somehow very common in industry and maybe some people meet similar situation before.
Perhaps use Bayesian Optimization, where you solve to get the inputs to get you closest to the targeted Y value?