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Bayesian ensemble of regression trees for multinomial probit and quantile regression

机译：多项式概率和分位数回归的回归树的贝叶斯合奏

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摘要

This dissertation proposes multinomial probit Bayesian additive regression trees (MPBART), ordered multiclass Bayesian additive classification trees (O-MBACT) and Bayesian quantile additive regression trees (BayesQArt) as extensions of BART---Bayesian additive regression trees for tackling multinomial choice, multiclass classification, ordinal regression and quantile regression problems. The proposed models exhibit very good predictive performances. In particular, ranking among the top performing procedures when non-linear relationships exist between the response and the predictors. The proposed procedures can readily be applied on data sets with the number of predictors larger than the number of observations.;MPBART is sufficiently flexible to allow inclusion of predictors that describe the observed units as well as the available choice alternatives and it can also be used as a general multiclass classification procedure. Through two simulation studies and four real data examples, we show that MPBART exhibits very good out-of-sample predictive performance in comparison to other discrete choice and multiclass classification methods. To implement MPBART, the R package mpbart is freely available from CRAN repositories.;When ordered gradation is exhibited by a multinomial response, ordinal regression is an appealing framework. Ensemble of trees models, while widely used for binary classification, multiclass classification and continuous response regression, have not been extensively applied to solve ordinal regression problems. This work fills this void with Bayesian sum of regression trees. The predictive performance of our ordered Bayesian ensemble of trees model is illustrated through simulation studies and real data applications.;Ensemble of regression trees have become popular statistical tools for the estimation of conditional mean given a set of predictors. However, quantile regression trees and their ensembles have not yet garnered much attention despite the increasing popularity of the linear quantile regression model. This work proposes a Bayesian quantile additive regression trees model that shows very good predictive performance illustrated using simulation studies and real data applications. Further extension to tackle binary classification problems is also considered.
机译：本文提出了多项式概率贝叶斯加性回归树（MPBART），有序多类贝叶斯加性分类树（O-MBACT）和贝叶斯分位数加性回归树（BayesQArt）作为BART的扩展-贝叶斯加性回归树用于处理多项式选择，多类分类，序数回归和分位数回归问题。所提出的模型表现出非常好的预测性能。特别是，在响应和预测变量之间存在非线性关系时，在执行效果最好的过程中排名。所建议的程序可以容易地应用于预测变量数量大于观测数量的数据集。； MPBART具有足够的灵活性，可以包含描述观测单位以及可用选择替代方案的预测变量，也可以使用作为通用的多类分类程序。通过两次仿真研究和四个真实数据示例，我们表明MPBART与其他离散选择和多类分类方法相比，具有非常好的样本外预测性能。要实现MPBART，可从CRAN信息库免费获得R包mpbart。当多项式响应显示有序灰度时，有序回归是一个吸引人的框架。树木模型集成虽然广泛用于二元分类，多类分类和连续响应回归，但尚未广泛应用于解决有序回归问题。这项工作用回归树的贝叶斯和填补了这一空白。通过仿真研究和实际数据应用，说明了我们的有序贝叶斯集合树模型的预测性能。回归树的集合已成为流行的统计工具，用于给定一组预测子的条件均值估计。然而，尽管线性分位数回归模型越来越受欢迎，但分位数回归树及其合奏尚未引起人们的广泛关注。这项工作提出了一个贝叶斯分位数加性回归树模型，该模型通过仿真研究和实际数据应用展示了很好的预测性能。还考虑了进一步扩展以解决二进制分类问题。

著录项

  • 作者

    Kindo, Bereket P.;

  • 作者单位

    University of South Carolina.;

  • 授予单位 University of South Carolina.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2016
  • 页码 112 p.
  • 总页数 112
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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