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    Assessing variable activity for Bayesian regression trees

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    Type
    Article
    Authors
    Horiguchi, Akira cc
    Pratola, Matthew T. cc
    Santner, Thomas J. cc
    KAUST Grant Number
    CRG
    Date
    2020-12-07
    Preprint Posting Date
    2020-05-27
    Online Publication Date
    2020-12-07
    Print Publication Date
    2021-03
    Embargo End Date
    2022-12-08
    Permanent link to this record
    http://hdl.handle.net/10754/663636
    
    Metadata
    Show full item record
    Abstract
    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.
    Citation
    Horiguchi, A., Pratola, M. T., & Santner, T. J. (2021). Assessing variable activity for Bayesian regression trees. Reliability Engineering & System Safety, 207, 107391. doi:10.1016/j.ress.2020.107391
    Sponsors
    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.
    Publisher
    Elsevier BV
    Journal
    Reliability Engineering & System Safety
    DOI
    10.1016/j.ress.2020.107391
    arXiv
    2005.13622
    Additional Links
    https://linkinghub.elsevier.com/retrieve/pii/S0951832020308784
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.ress.2020.107391
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