SHAP values which are essentially the variable importance at a local level where each variable's importance is assessed by different in probability outcome of a model with and without the variable. I understand that if a baseline model gives probability for example 0.70 for an observation. If we add variable X1 & X2 to it and re-build the model, its probability prediction of the same observation jumps to 0.90 where X1 (shap value could be 0.15) and X2 ( shap value 0.05) or simple rule where X1(shap) + X2(shap) = P(with variable model) - P(without variable model). How is then intuitively different from information gain in a decision tree apart from the fact that decision tree just splits by one variable at one node and SHAP values are combination that together give the overall change in probability i.e. 0.70 to 0.90


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