Sadly, I think this formula is wrong, which kinda of invalidates the whole piece..

For \sum{impact_i} =predicted_proba (which if that's not the case what's the point of this?!), we would need f(\sum{shap_i} - shap_j) = f(\sum{shap_i}) - f(shap_j) , which is not true because the function is nonlinear.

If we just write out the formula we see it doesn't cancel out.

let S_k = \sum{shap_i} - shap_k

\sum_k{impact_k} = \sum_k{ (prob - f(S_k)) }= |Feature_Set| * prob - \sum_k f(S_k)

The only way that would cancel out is if the function f is linear.