Does the reliability of feature importance depend on model performance? I am wondering if there is a relationship between the performance quality of a predictive model (e.g., a classifier) and the reliability of corresponding feature importance values?
To give an example: I created two binary classifiers using two different sets of features. One classifier performs slightly better than the other. However, both perform not that great (balanced accuracies are around 65% and 55%). I calculated feature importance scores using permutation importance. Is it valid to say that both lists of importance values are equally reliable/interpretable?
Any help or literature recommendations are highly appreciated!
 A: First of all permutation importance does not take into account some kinds of dependencies. For example if feature 1 and 2 are only important when they are both present, then with permutation importance you will never see this.
Besides for that - it depends by what you mean when you say feature importance. If you mean how important a feature is for a model, then it does not matter how well performing the model is. If you mean how strong of a connection does the feature have with the target, then yes a model's feature importance score is less relevant for less well performing model.
Besides that- you want help or recommendations in what?
A: Yes feature importance is computed based on the impact on performance of the model. A feature with high importance means it has large impact on the performance for example, from 90% it came down to 70%. And when the performance measures are itself on the lower side, impact on performance does not make much sense. In a way you could relate performance and feature importance.
