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I am interested in reasons as to why different feature importance methods might give different feature rankings. In particular, Shapley values vs other methods such as weight/gain from OOB score.

Consider the example below using the California house price dataset. Here for illustrative purposes I have fitted a gradient boosting model. Please note that this example is illustrative, and I am interested in how the two methods could disagree assuming that the gradient boosting model is tuned with no bias/variance issues.

The feature importance calculated when constructing the gradient boosting model is given below:

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However the Shapley values calculated give different feature ranking all together.

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My thinking is that it is due to the different calculation methods. If the Shapley value of a feature is calculated as the average change in the prediction that a coalition (subset of features) receives when a feature is added (i.e. weighted and summed over all possible feature value combinations), then perhaps it should not agree with other feature importance methods (as it is averaged over all feature combinations).

Does anyone know why feature importance calculation methods would not agree? Any literature on this topic people can provide would be greatly appreciated.

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    $\begingroup$ Yes. The two approaches are different, so do the results. Throw in permutation importance and you get a third variant. $\endgroup$
    – Michael M
    May 13, 2020 at 17:03
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    $\begingroup$ Feature importance measures are not like other calculations in statistics in that they are not estimates of any real world parameters. They are ad-hoc attempts to capture some essence of the undefined, fuzzy concept of "feature importance", whatever that means. So where, say, different estimators of a population mean should roughly agree (they are estimates of the same underlying concept/value), feature importance measures are not like this. $\endgroup$ May 13, 2020 at 17:07

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