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

Variable importance is central to scientific studies, including the social sciences and causal inference, healthcare, and in other domains. However, current notions of variable importance are often tied to a specific predictive model. This is problematic: what if there were multiple well-performing predictive models, 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 model whether a variable is always important in predicting the outcome. Rather than depending on variable importance for a single predictive model, we would like to explore variable importance for all approximately-equally-accurate predictive models. This work introduces the concept of a variable importance cloud, which maps every variable to its importance for every good predictive model. We show properties of the variable importance cloud and draw connections other areas of statistics. We introduce variable importance diagrams as a projection of the variable importance cloud into two dimensions for visualization purposes. Experiments with criminal justice and marketing data illustrate how variables can change dramatically in importance for approximately-equally-accurate predictive models.