Particle Gibbs for Bayesian Additive Regression Trees

Balaji Lakshminarayanan, Daniel Roy, Yee Whye Teh
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:553-561, 2015.

Abstract

Additive regression trees are flexible non-parametric models and popular off-the-shelf tools for real-world non-linear regression. In application domains, such as bioinformatics, where there is also demand for probabilistic predictions with measures of uncertainty, the Bayesian additive regression trees (BART) model, introduced by Chipman et al. (2010), is increasingly popular. As data sets have grown in size, however, the standard Metropolis–Hastings algorithms used to per- form inference in BART are proving inadequate. In particular, these Markov chains make local changes to the trees and suffer from slow mixing when the data are high- dimensional or the best-fitting trees are more than a few layers deep. We present a novel sampler for BART based on the Particle Gibbs (PG) algorithm (Andrieu et al., 2010) and a top-down particle filtering algorithm for Bayesian decision trees (Lakshminarayanan et al., 2013). Rather than making local changes to individual trees, the PG sampler proposes a complete tree to fit the residual. Experiments show that the PG sampler outperforms existing samplers in many settings.

Cite this Paper


BibTeX
@InProceedings{pmlr-v38-lakshminarayanan15, title = {{Particle Gibbs for Bayesian Additive Regression Trees}}, author = {Balaji Lakshminarayanan and Daniel Roy and Yee Whye Teh}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {553--561}, year = {2015}, editor = {Guy Lebanon and S. V. N. Vishwanathan}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/lakshminarayanan15.pdf}, url = { http://proceedings.mlr.press/v38/lakshminarayanan15.html }, abstract = {Additive regression trees are flexible non-parametric models and popular off-the-shelf tools for real-world non-linear regression. In application domains, such as bioinformatics, where there is also demand for probabilistic predictions with measures of uncertainty, the Bayesian additive regression trees (BART) model, introduced by Chipman et al. (2010), is increasingly popular. As data sets have grown in size, however, the standard Metropolis–Hastings algorithms used to per- form inference in BART are proving inadequate. In particular, these Markov chains make local changes to the trees and suffer from slow mixing when the data are high- dimensional or the best-fitting trees are more than a few layers deep. We present a novel sampler for BART based on the Particle Gibbs (PG) algorithm (Andrieu et al., 2010) and a top-down particle filtering algorithm for Bayesian decision trees (Lakshminarayanan et al., 2013). Rather than making local changes to individual trees, the PG sampler proposes a complete tree to fit the residual. Experiments show that the PG sampler outperforms existing samplers in many settings.} }
Endnote
%0 Conference Paper %T Particle Gibbs for Bayesian Additive Regression Trees %A Balaji Lakshminarayanan %A Daniel Roy %A Yee Whye Teh %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-lakshminarayanan15 %I PMLR %P 553--561 %U http://proceedings.mlr.press/v38/lakshminarayanan15.html %V 38 %X Additive regression trees are flexible non-parametric models and popular off-the-shelf tools for real-world non-linear regression. In application domains, such as bioinformatics, where there is also demand for probabilistic predictions with measures of uncertainty, the Bayesian additive regression trees (BART) model, introduced by Chipman et al. (2010), is increasingly popular. As data sets have grown in size, however, the standard Metropolis–Hastings algorithms used to per- form inference in BART are proving inadequate. In particular, these Markov chains make local changes to the trees and suffer from slow mixing when the data are high- dimensional or the best-fitting trees are more than a few layers deep. We present a novel sampler for BART based on the Particle Gibbs (PG) algorithm (Andrieu et al., 2010) and a top-down particle filtering algorithm for Bayesian decision trees (Lakshminarayanan et al., 2013). Rather than making local changes to individual trees, the PG sampler proposes a complete tree to fit the residual. Experiments show that the PG sampler outperforms existing samplers in many settings.
RIS
TY - CPAPER TI - Particle Gibbs for Bayesian Additive Regression Trees AU - Balaji Lakshminarayanan AU - Daniel Roy AU - Yee Whye Teh BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-lakshminarayanan15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 553 EP - 561 L1 - http://proceedings.mlr.press/v38/lakshminarayanan15.pdf UR - http://proceedings.mlr.press/v38/lakshminarayanan15.html AB - Additive regression trees are flexible non-parametric models and popular off-the-shelf tools for real-world non-linear regression. In application domains, such as bioinformatics, where there is also demand for probabilistic predictions with measures of uncertainty, the Bayesian additive regression trees (BART) model, introduced by Chipman et al. (2010), is increasingly popular. As data sets have grown in size, however, the standard Metropolis–Hastings algorithms used to per- form inference in BART are proving inadequate. In particular, these Markov chains make local changes to the trees and suffer from slow mixing when the data are high- dimensional or the best-fitting trees are more than a few layers deep. We present a novel sampler for BART based on the Particle Gibbs (PG) algorithm (Andrieu et al., 2010) and a top-down particle filtering algorithm for Bayesian decision trees (Lakshminarayanan et al., 2013). Rather than making local changes to individual trees, the PG sampler proposes a complete tree to fit the residual. Experiments show that the PG sampler outperforms existing samplers in many settings. ER -
APA
Lakshminarayanan, B., Roy, D. & Teh, Y.W.. (2015). Particle Gibbs for Bayesian Additive Regression Trees. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:553-561 Available from http://proceedings.mlr.press/v38/lakshminarayanan15.html .

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