Feature selection for regression Suppose I have a response variable y and and a set of feature variables (x1, x2 ... xn). I wish to find which of x1...xn are the best features for y in a regression problem (the relationship might not be linear). 
Is there any way I can do this kind of feature selection without using any correlation measure or regression function in the process (i.e. I cannot use any filter or wrapper methods)?
You can train a LightGBM Regressor. LightGBM Regressor feature selection methods embbed in it. You can direct plot them to see which features are important.
See this link.
LightGBM Plot Importance