BART: Bayesian additive regression trees. We develop a Bayesian “sum-of-trees” model where each tree is constrained by a regularization prior to be a weak learner, and fitting and inference are accomplished via an iterative Bayesian backfitting MCMC algorithm that generates samples from a posterior. Effectively, BART is a nonparametric Bayesian regression approach which uses dimensionally adaptive random basis elements. Motivated by ensemble methods in general, and boosting algorithms in particular, BART is defined by a statistical model: a prior and a likelihood. This approach enables full posterior inference including point and interval estimates of the unknown regression function as well as the marginal effects of potential predictors. By keeping track of predictor inclusion frequencies, BART can also be used for model-free variable selection. BART’s many features are illustrated with a bake-off against competing methods on 42 different data sets, with a simulation experiment and on a drug discovery classification problem.

References in zbMATH (referenced in 83 articles )

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  1. Francom, Devin; Sansó, Bruno; Kupresanin, Ana: Landmark-warped emulators for models with misaligned functional response (2022)
  2. Wu, Suofei; Hannig, Jan; Lee, Thomas C. M.: Uncertainty quantification for honest regression trees (2022)
  3. Castillo, Ismaël; Ročková, Veronika: Uncertainty quantification for Bayesian CART (2021)
  4. Glynn, Chris; Byrne, Thomas H.; Culhane, Dennis P.: Inflection points in community-level homeless rates (2021)
  5. Maillart, Arthur: Toward an explainable machine learning model for claim frequency: a use case in car insurance pricing with telematics data (2021)
  6. Starling, Jennifer E.; Murray, Jared S.; Lohr, Patricia A.; Aiken, Abigail R. A.; Carvalho, Carlos M.; Scott, James G.: Targeted smooth Bayesian causal forests: an analysis of heterogeneous treatment effects for simultaneous vs. interval medical abortion regimens over gestation (2021)
  7. Sun, Yilun; Wang, Lu: Stochastic tree search for estimating optimal dynamic treatment regimes (2021)
  8. Tabak, Esteban G.; Trigila, Giulio; Zhao, Wenjun: Data driven conditional optimal transport (2021)
  9. Zhang, Yuyang; Schnell, Patrick; Song, Chi; Huang, Bin; Lu, Bo: Subgroup causal effect identification and estimation via matching tree (2021)
  10. Afrabandpey, Homayun; Peltola, Tomi; Piironen, Juho; Vehtari, Aki; Kaski, Samuel: A decision-theoretic approach for model interpretability in Bayesian framework (2020)
  11. Antonelli, Joseph; Mazumdar, Maitreyi; Bellinger, David; Christiani, David; Wright, Robert; Coull, Brent: Estimating the health effects of environmental mixtures using Bayesian semiparametric regression and sparsity inducing priors (2020)
  12. Behrens, Christoph; Pierdzioch, Christian; Risse, Marian: Do German economic research institutes publish efficient growth and inflation forecasts? A Bayesian analysis (2020)
  13. Fisher, Jared D.; Puelz, David W.; Carvalho, Carlos M.: Monotonic effects of characteristics on returns (2020)
  14. Franks, AlexanderM.; D’Amour, Alexander; Feller, Avi: Flexible sensitivity analysis for observational studies without observable implications (2020)
  15. Hahn, P. Richard; Murray, Jared S.; Carvalho, Carlos M.: Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects (with discussion) (2020)
  16. Hu, Ruimeng: Deep learning for ranking response surfaces with applications to optimal stopping problems (2020)
  17. Kaandorp, Mikael L. A.; Dwight, Richard P.: Data-driven modelling of the Reynolds stress tensor using random forests with invariance (2020)
  18. Kowal, Daniel R.; Canale, Antonio: Simultaneous transformation and rounding (STAR) models for integer-valued data (2020)
  19. Lopes, Miles E.; Wu, Suofei; Lee, Thomas C. M.: Measuring the algorithmic convergence of randomized ensembles: the regression setting (2020)
  20. Mourtada, Jaouad; Gaïffas, Stéphane; Scornet, Erwan: Minimax optimal rates for Mondrian trees and forests (2020)

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