Assessing variable activity for Bayesian regression trees

Akira Horiguchi, Matthew T. Pratola and Thomas J. Santner

Reliability Engineering and System Safety, 2021, vol. 207, issue C

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 SobolÌ 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 SobolÌ 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) SobolÌ indices and one-way counts. We also introduce a novel ranking method, and use this to demonstrate that the proposed indices preserve the SobolÌ -based rank order of variable importance. Finally, we compare these methods using analytic test functions and the En-ROADS climate impacts simulator.

Keywords: Bayesian Additive Regression Trees; Global sensitivity analysis; SobolÌ indices; Nonparametric; Variable importance; Variable activity (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0951832020308784
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:207:y:2021:i:c:s0951832020308784

DOI: 10.1016/j.ress.2020.107391

Access Statistics for this article

Reliability Engineering and System Safety is currently edited by Carlos Guedes Soares

More articles in Reliability Engineering and System Safety from Elsevier
Bibliographic data for series maintained by Catherine Liu ().