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Variable importance is central to scientific studies, including the socialsciences and causal inference, healthcare, and other domains. However, currentnotions of variable importance are often tied to a specific predictive model.This is problematic: what if there were multiple well-performing predictivemodels, and a specific variable is important to some of them and not to others?In that case, we may not be able to tell from a single well-performing modelwhether a variable is always important in predicting the outcome. Rather thandepending on variable importance for a single predictive model, we would liketo explore variable importance for all approximately-equally-accuratepredictive models. This work introduces the concept of a variable importancecloud, which maps every variable to its importance for every good predictivemodel. We show properties of the variable importance cloud and draw connectionsto other areas of statistics. We introduce variable importance diagrams as aprojection of the variable importance cloud into two dimensions forvisualization purposes. Experiments with criminal justice, marketing data, andimage classification tasks illustrate how variables can change dramatically inimportance for approximately-equally-accurate predictive models

Variable Importance Clouds: A Way to Explore Variable Importance for the Set of Good Models