I give a simple example: I have a set of houses with different features (# rooms, perimeter, # neighbours, etc...), almost 15, and a price value for each house. The features are also quite correlated (i.e. perimeter is often correlated with #rooms). I want to establish what are the main features (or non-linear combination of them) that determine the price.
In a linear case, for instance, I can compute a Lasso regression and see the importance of each feature through the coefficients. In my case, every feature (or maybe combination of them) has a non linear impact. For example, the # of neighbours can have a quadratic impact (increase the price if #neighbours < 10, and decrease the price if > 10).
I want to identify the main important relationship among the features and the prices. I don't need a predictor. For example, at the end I will discover that the price depends principally by #rooms/perimeter and #neighbours^2.
I was thinking to apply Kernel methods, in combination with regression or PCA. But I don't know a lot about kernel methods.
Thank you in advance.