Variable selection with ABC Bayesian forests

Yi Liu, Veronika Ročková and Yuexi Wang

Journal of the Royal Statistical Society Series B, 2021, vol. 83, issue 3, 453-481

Abstract: Few problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants thereof. In this work, we abandon the linear model framework, which can be quite detrimental when the covariates impact the outcome in a non‐linear way, and turn to tree‐based methods for variable selection. Such variable screening is traditionally done by pruning down large trees or by ranking variables based on some importance measure. Despite heavily used in practice, these ad hoc selection rules are not yet well understood from a theoretical point of view. In this work, we devise a Bayesian tree‐based probabilistic method and show that it is consistent for variable selection when the regression surface is a smooth mix of p > n covariates. These results are the first model selection consistency results for Bayesian forest priors. Probabilistic assessment of variable importance is made feasible by a spike‐and‐slab wrapper around sum‐of‐trees priors. Sampling from posterior distributions over trees is inherently very difficult. As an alternative to Markov Chain Monte Carlo (MCMC), we propose approximate Bayesian computation (ABC) Bayesian forests, a new ABC sampling method based on data‐splitting that achieves higher ABC acceptance rate. We show that the method is robust and successful at finding variables with high marginal inclusion probabilities. Our ABC algorithm provides a new avenue towards approximating the median probability model in non‐parametric setups where the marginal likelihood is intractable.

Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1111/rssb.12423

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:bla:jorssb:v:83:y:2021:i:3:p:453-481

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().