First of all, the package is great! I only have a few technical questions with regards to the kernel.py code of the SHAP package

I am trying to understand how SHAP values are computed by the Kernel SHAP method from the SHAP package. As I understand it, you solve a weighted linear regression to attain SHAP values, using phi = ((X'WX)^-1)X'Wy.

At a high level, wha I gather so far - especially looking at lines 296-343, in combination with the referenced functions:

• nsamples determines how many permutations out of the M! possible feature orderings are regarded
• (nsamples X number of background samples (size N))-number of y-values are computed, whereby each N-sized set is the result of a different feature ordering (i.e. different features "switched on/off") for each row of background samples (size N) and the empirical mean is taken for each of the N-sized sets, producing nsamples empirical means
• a diff-in-diff is calculated, to match feature contributions to individual features ( E[y|X_s] - f_null ) - maskMatrix*( f_x - f_null)
• then a WLS is solved, providing the SHAP values

Did I understand this correctly?

If so, there are a few things, however, I would like to ask:

• if the feature space is fairly large (say 100+), since nsamples restricts variety of feature permutations computed and since the feature permutations are regarded in a sequential manner, (i.e. first only subsets of size 1, 2, ...), does this not disregard interaction effects between features? Even though this is partially accounted for as I understand by

"add random samples from what is left of the subset space"

Because even for 47 features onwards, if I understand it correctly, only subsets of size 1 (and its complement) are considered fully.

• why is one variable eliminated later on in the solve function?

"eliminate one variable with the constraint that all features sum to the output"

• what is the intuition behind multiplying the weight vector by 2?

Thank you very much in advance!