1,022
Views
5
CrossRef citations to date
0
Altmetric
Theory and Methods

Adaptive Conditional Distribution Estimation with Bayesian Decision Tree Ensembles

, &
Pages 2129-2142 | Received 22 Feb 2020, Accepted 26 Jan 2022, Published online: 18 Mar 2022

References

  • Adler, R. J., Taylor, J. E., and Worsley, K. J. (2015), “Applications of Random Fields and Geometry: Foundations and Case Studies,” Preprint. Available at https://web.stanford.edu/class/stats317/hrf.pdf.
  • Albert, J. H., and Chib, S. (1993), “Bayesian Analysis of Binary and Polychotomous Response Data,” Journal of the American Statistical Association, 88, 669–679. DOI: 10.1080/01621459.1993.10476321.
  • Angrist, J., Chernozhukov, V., and Fernández-Val, I. (2006), “Quantile Regression Under Misspecification, with an Application to the US Wage Structure,” Econometrica, 74, 539–563. DOI: 10.1111/j.1468-0262.2006.00671.x.
  • Antoniano-Villalobos, I., Wade, S., and Walker, S. G. (2014), “A Bayesian Nonparametric Regression Model with Normalized Weights: A Study of Hippocampal Atrophy in Alzheimer’s Disease,” Journal of the American Statistical Association, 109, 477–490. DOI: 10.1080/01621459.2013.879061.
  • Azzalini, A. (2013), The Skew-Normal and Related Families (Vol. 3), Cambridge: Cambridge University Press.
  • Basak, P., Linero, A., Sinha, D., and Lipsitz, S. (2021), “Semiparametric Analysis of Clustered Interval-Censored Survival Data Using Soft Bayesian Additive Regression Trees (SBART),” Biometrics. Advance online publication. DOI: 10.1111/biom.13478.
  • Breiman, L. (2001), “Random Forests,” Machine Learning, 45, 5–32. DOI: 10.1023/A:1010933404324.
  • Chipman, H. A., George, E. I., and McCulloch, R. E. (2010), “BART: Bayesian Additive Regression Trees,” The Annals of Applied Statistics, 4, 266–298. DOI: 10.1214/09-AOAS285.
  • Chung, Y., and Dunson, D. B. (2009), “Nonparametric Bayes Conditional Distribution Modeling with Variable Selection,” Journal of the American Statistical Association, 104, 1646–1660. DOI: 10.1198/jasa.2009.tm08302.
  • Cohen, A. K., Rai, M., Rehkopf, D. H., and Abrams, B. (2013), “Educational Attainment and Obesity: A Systematic Review,” Obesity Reviews, 14, 989–1005. DOI: 10.1111/obr.12062.
  • Dunson, D. B., and Park, J.-H. (2008), “Kernel Stick-Breaking Processes,” Biometrika, 95, 307–323. DOI: 10.1093/biomet/asn012.
  • Dunson, D. B., Pillai, N., and Park, J. H. (2007), “Bayesian Density Regression,” Journal of the Royal Statistical Society, Series B, 69, 163–183. DOI: 10.1111/j.1467-9868.2007.00582.x.
  • Friedman, J. H. (1991), “Multivariate Adaptive Regression Splines,” The Annals of Statistics, 19, 1–67. DOI: 10.1214/aos/1176347963.
  • Ghosal, S., Ghosh, J. K., and Ramamoorthi, R. V. (1999), “Posterior Consistency of Dirichlet Mixtures in Density Estimation,” Annals of Statistics, 27, 143–158.
  • Ghosal, S., Ghosh, J. K., and van der Vaart, A. W. (2000), “Convergence Rates of Posterior Distributions,” Annals of Statistics, 28, 500–531.
  • Hahn, P. R., and Carvalho, C. M. (2015). “Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective,” Journal of the American Statistical Association, 110, 435–448. DOI: 10.1080/01621459.2014.993077.
  • Jara, A., Hanson, T. E., Quintana, F. A., Müller, P., and Rosner, G. L. (2011), Dppackage: Bayesian Semi- and Nonparametric Modeling in R,” Journal of Statistical Software, 40, 1–30. DOI: 10.18637/jss.v040.i05.
  • Kundu, S., and Dunson, D. B. (2014), “Latent Factor Models for Density Estimation,” Biometrika, 101, 641–654. DOI: 10.1093/biomet/asu019.
  • Linero, A. R. (2018), “Bayesian Regression Trees for High-Dimensional Prediction and Variable Selection,” Journal of the American Statistical Association, 113, 626–636. DOI: 10.1080/01621459.2016.1264957.
  • Linero, A. R., Basak, P., Li, Y., and Sinha, D. (2021), “Bayesian Survival Tree Ensembles with Submodel Shrinkage,” Bayesian Analysis. Advance online publication. DOI: 10.1214/21-BA1285.
  • Linero, A. R., and Yang, Y. (2018), “Bayesian Regression Tree Ensembles that Adapt to Smoothness and Sparsity,” Journal of the Royal Statistical Society, Series B, 80, 1087–1110. DOI: 10.1111/rssb.12293.
  • MacEachern, S. N. (1999), “Dependent Nonparametric Processes,” in ASA Proceedings of the Section on Bayesian Statistical Science, pp. 50–55.
  • Müller, P., Erkanli, A., and West, M. (1996), “Bayesian Curve Fitting Using Multivariate Normal Mixtures,” Biometrika, 83, 67–79.
  • Murray, I., MacKay, D., and Adams, R. P. (2009), “The Gaussian Process Density Sampler,” in Advances in Neural Information Processing Systems (Vol. 21), eds. D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, Curran Associates, Inc.
  • Pati, D., Dunson, D. B., and Tokdar, S. T. (2013), “Posterior Consistency in Conditional Distribution Estimation,” Journal of Multivariate Analysis, 116, 456–472. DOI: 10.1016/j.jmva.2013.01.011.
  • Pospisil, T., and Lee, A. B. (2018), “RFCDE: Random Forests for Conditional Density Estimation,” arXiv preprint arXiv:1804.05753.
  • Pratola, M. T., Chipman, H. A., George, E. I., and McCulloch, R. E. (2020), “Heteroscedastic BART via Multiplicative Regression Trees,” Journal of Computational and Graphical Statistics, 29, 405–417. DOI: 10.1080/10618600.2019.1677243.
  • Rahimi, A., and Recht, B. (2008), “Random Features for Large-Scale Kernel Machines,” in Advances in Neural Information Processing Systems (Vol. 20), eds. J. Platt, D. Koller, Y. Singer, and S. Roweis, Curran Associates, Inc.
  • Rao, V., Lin, L., and Dunson, D. B. (2016), “Data Augmentation for Models Based on Rejection Sampling,” Biometrika, 103, 319–335. DOI: 10.1093/biomet/asw005.
  • Ravikumar, P., Liu, H., Lafferty, J., and Wasserman, L. (2007), “SPAM: Sparse Additive Models,” in Proceedings of the 20th International Conference on Neural Information Processing Systems, pp. 1201–1208.
  • Reich, B. J., Fuentes, M., and Dunson, D. B. (2011), “Bayesian Spatial Quantile Regression,” Journal of the American Statistical Association, 106, 6–20. DOI: 10.1198/jasa.2010.ap09237.
  • Riihimäki, J., Vehtari, A. (2014). “Laplace Approximation for Logistic Gaussian Process Density Estimation and Regression,” Bayesian Analysis, 9, 425–448. DOI: 10.1214/14-BA872.
  • Ročková, V., and van der Pas, S. (2020), “Posterior Concentration for Bayesian Regression Trees and Forests,” The Annals of Statistics, 48, 2108–2131. DOI: 10.1214/19-AOS1879.
  • Rodríguez, A., and Dunson, D. B. (2011), “Nonparametric Bayesian Models Through Probit Stick-Breaking Processes,” Bayesian Analysis, 6, 145 – 177.
  • Sethuraman, J. (1994), “A Constructive Definition of Dirichlet Priors,” Statistica Sinica, 4, 639–650.
  • Shahbaba, B., and Neal, R. M. (2009), “Nonlineaer Models Using Dirichlet Process Mixtures,” Journal of Machine Learning Research, 10, 1829–1850.
  • Starling, J. E., Murray, J. S., Carvalho, C. M., Bukowski, R. K., and Scott, J. G. (2020), “BART with Targeted Smoothing: An Analysis of Patient-Specific Stillbirth Risk,” The Annals of Applied Statistics, 14, 28–50. DOI: 10.1214/19-AOAS1268.
  • Tokdar, S. T., Zhu, Y. M., Ghosh, J. K. (2010), “Bayesian Density Regression with Logistic Gaussian Process and Subspace Projection,” Bayesian Analysis, 5, 319–344. DOI: 10.1214/10-BA605.
  • van der Vaart, A. W., and van Zanten, J. H. (2008), “Rates of Contraction of Posterior Distributions Based on Gaussian Process Priors,” The Annals of Statistics, 36, 1435–1463. DOI: 10.1214/009053607000000613.
  • Wade, S., Dunson, D. B., Petrone, S., and Trippa, L. (2014), “Improving Prediction from Dirichlet Process Mixtures via Enrichment,” The Journal of Machine Learning Research, 15, 1041–1071.
  • Woody, S., Carvalho, C. M., and Murray, J. S. (2020), “Model Interpretation Through Lower-Dimensional Posterior Summarization,” Journal of Computational and Graphical Statistics, 30, 144–161. DOI: 10.1080/10618600.2020.1796684.
  • Yang, Y., and Tokdar, S. T. (2015), “Minimax-Optimal Nonparametric Regression in High Dimensions,” The Annals of Statistics, 43, 652–674. DOI: 10.1214/14-AOS1289.
  • Yang, Y., and Tokdar, S. T. (2017), “Joint Estimation of Quantile Planes Over Arbitrary Predictor Spaces,” Journal of the American Statistical Association, 112, 1107–1120. DOI: 10.1080/01621459.2016.1192545.
  • Yang, Y., Wang, H. J., and He, X. (2016), “Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood,” International Statistical Review, 84, 327–344. DOI: 10.1111/insr.12114.
  • Yu, K., and Moyeed, R. A. (2001), “Bayesian Quantile Regression,” Statistics & Probability Letters, 54, 437–447.
  • Zhu, R., and Kosorok, M. R. (2012), “Recursively Imputed Survival Trees,” Journal of the American Statistical Association, 107, 331–340. DOI: 10.1080/01621459.2011.637468.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.