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Abstract:
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Bayesian Additive Regression Trees (BART) are non-parametric models that can capture complex exogenous variable effects. In any regression problem, it is often of interest to learn which variables are most active. Variable activity in BART is usually measured by counting the number of times a tree splits for each variable. Despite their convenience, one-way counts are statistically unjustified, cannot distinguish between main effects and interactions, and become inflated when measuring interaction effects. An alternative method well-established in the literature is Sobol' indices, a variance-based global sensitivity analysis technique. However, these indices often require Monte Carlo integration, which can be computationally expensive. This paper provides computationally feasible analytic expressions for Sobol' indices for BART predictors. Furthermore, we will show a fascinating connection between main-effects Sobol' indices and one-way counts. We also create a ranking method to demonstrate that the proposed indices preserve the Sobol'-based rank order of variable importance. Finally, we compare these methods using analytic test functions and the En-ROADS climate impacts simulator.
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