I understand we can add $L_1$ or $L_2$ regularization to linear regression (Lasso and Ridge regression). In addition, it is possible to restrict the coefficient to be integers (see this post).
However, is there any related work to add special constraints to enforce the relationship between features?
- For example, suppose, I know feature 1 is much important than feature 2, so I want to make $\beta_1 \in [10,20]$ and $\beta_2 \in [1,2]$ as a constraint in the model.
- Another example would be, I think feature 1 is similar to feature 2. So, I want $|\beta_1-\beta_2|<c$.
If there is related work, please provide a link to the paper.
If not, how do people deal with incorporating domain knowledge about the importance of the feature to the model coefficient?