# SHAP values under multicolinearity/feature dependence

My task is to explain individual predictions, but having read the original paper and sifted through the internet, I am still unsure whether using something like TreeSHAP can help me with the situation of correlated features.

Currently, I am using regularization to help with multicolinearity, and then using KernelSHAP on a tree based model (AWS has only KernelSHAP implemented currently), but with correlation amongst features, I am unsure whether treeSHAP would help me with the problem. If not, how should I proceed?

Quoting from Christopher Molnar's explainability book, "KernelSHAP ignores feature dependence. Most other permutation based interpretation methods have this problem. By replacing feature values with values from random instances, it is usually easier to randomly sample from the marginal distribution. However, if features are dependent, e.g. correlated, this leads to putting too much weight on unlikely data points. TreeSHAP solves this problem by explicitly modeling the conditional expected prediction.

TreeSHAP can produce unintuitive feature attributions. While TreeSHAP solves the problem of extrapolating to unlikely data points, it does so by changing the value function and therefore slightly changes the game. TreeSHAP changes the value function by relying on the conditional expected prediction. With the change in the value function, features that have no influence on the prediction can get a TreeSHAP value different from zero."

• You are good to bring up this concern. That’s one reason I use relative explained variation especially when the model is additive. It handles collinearities. Details are here. Commented Jul 10 at 15:49
• Thanks for the answer, this seems interesting. Although this requires refitting the original model multiple times? If so, that becomes infeasible in my case. Commented Jul 10 at 17:21
• Though the R rms package only implements this for a certain class of models, the basic idea only requires fitting a linear model to the predicted values once, if you are not getting uncertainty intervals for the relative explained variation indexes. The OLS linear model fit is quite fast. To get uncertainty intervals requires bootstrapping the process or using Bayes MCMC (the software allows for that). Commented Jul 11 at 11:47