Describe the problem

The current version of vector_auto_regression has an option to manually input l2_reg ridge penalty, but it does not check whether the matrix is rank deficient, in the case that the user chooses the default l2_reg of 0 (i.e., no regularization). This leads to a problem where the outputs are useless if the user does not realize that their matrix is rank deficient.

Describe your solution

I want to check for the matrix rank to ensure that it matches the number of nodes across all epochs. If any epoch is rank deficient, then for every epoch sklearn.linear_model.RidgeCV will be employed to automatically search for optimal alpha value, which will be used to regularize the matrix. This is more useful than asking the user to input an l2_reg because RidgeCV can solve for the best value using cross-validation.

Describe possible alternatives

A possible alternative would be to apply Ridge regression to all input matrices, regardless of whether they are full rank. Another option would be to remove the l2_reg value and use the automated search for all matrices if the user chooses.

Additional context

This issue was created based on this discussion post.

I am going to work on this and submit a pull request with my progress soon!