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. Such one-way counts have the advantage of fast computations. Despite their convenience, one-way counts have several issues. They are statistically unjustified, cannot distinguish between main effects and interaction effects, 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 analytic expressions for Sobol ́ indices for BART posterior samples. These expressions are easy to interpret and are computationally feasible. Furthermore, we will show a fascinating connection between first-order (main-effects) Sobol ́ indices and one-way counts. We also introduce a novel ranking method, and use this 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.
|Original language||English (US)|
|Journal||Reliability Engineering & System Safety|
|State||Published - Dec 7 2020|
Bibliographical noteKAUST Repository Item: Exported on 2021-02-09
Acknowledged KAUST grant number(s): CRG
Acknowledgements: We thank Professor Joseph Verducci for introducing A.H. to ranking models. We also thank the two referees and an Associate Editor for their comments, which have improved this paper. This work was supported by the Graduate School at The Ohio State University, USA; the National Science Foundation, USA [Agreements DMS-1916231, DMS-0806134, DMS-1310294]; the King Abdullah University of Science and Technology (KAUST), Saudi Arabia Office of Sponsored Research (OSR) [Award No. OSR-2018-CRG7-3800.3]; and the Isaac Newton Institute for Mathematical Sciences, United Kingdom.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.