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Quantifying variable importance is essential for answering high-stakesquestions in fields like genetics, public policy, and medicine. Current methodsgenerally calculate variable importance for a given model trained on a givendataset. However, for a given dataset, there may be many models that explainthe target outcome equally well; without accounting for all possibleexplanations, different researchers may arrive at many conflicting yet equallyvalid conclusions given the same data. Additionally, even when accounting forall possible explanations for a given dataset, these insights may notgeneralize because not all good explanations are stable across reasonable dataperturbations. We propose a new variable importance framework that quantifiesthe importance of a variable across the set of all good models and is stableacross the data distribution. Our framework is extremely flexible and can beintegrated with most existing model classes and global variable importancemetrics. We demonstrate through experiments that our framework recoversvariable importance rankings for complex simulation setups where other methodsfail. Further, we show that our framework accurately estimates the trueimportance of a variable for the underlying data distribution. We providetheoretical guarantees on the consistency and finite sample error rates for ourestimator. Finally, we demonstrate its utility with a real-world case studyexploring which genes are important for predicting HIV load in persons withHIV, highlighting an important gene that has not previously been studied inconnection with HIV. Code is available athttps://github.com/jdonnelly36/Rashomon_Importance_Distribution.

The Rashomon Importance Distribution: Getting RID of Unstable, Single Model-based Variable Importance