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    Assessing variable activity for Bayesian regression trees

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    Type
    Preprint
    Authors
    Horiguchi, Akira
    Pratola, Matthew T.
    Santner, Thomas J.
    Date
    2020-05-27
    Permanent link to this record
    http://hdl.handle.net/10754/663636
    
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    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 predictors. These expressions are easy to interpret and are computationally feasible. Furthermore, we will show a fascinating connection between 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.
    Sponsors
    A.H. would like to acknowledge the Graduate School at The Ohio State University for support during the dissertation year. The work of M.T.P. was supported in part by the National Science Foundation under Agreement DMS-1916231 and in part by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-2018-CRG7-3800.3. T.J.S. would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme on Uncertainty Quantification when work on this paper was undertaken. This research was also sponsored, in part, by the National Science Foundation under Agreements DMS-0806134 and DMS-1310294 (The Ohio State University).
    Publisher
    arXiv
    arXiv
    arXiv:2005.13622
    Additional Links
    https://arxiv.org/pdf/2005.13622
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