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首页> 外文学位 >Quantile regression trees, statistical applications of CUDA programming and identification of active effects without sparsity assumption.
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Quantile regression trees, statistical applications of CUDA programming and identification of active effects without sparsity assumption.

机译：分位数回归树，CUDA编程的统计应用以及无需稀疏假设的主动效应的识别。

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摘要

We introduce binary regression tree methods for estimating quantiles. Quantile regression trees can capture the relationship between the response and the predictors at different quantiles of the distribution. The trees are constructed by recursively partitioning the predictor space into terminal nodes and fitting linear quantile regression models to the terminal nodes. We provide two options to choose the partition: (1) search over all the predictors and all possible splits to choose the predictor and split that minimizes the quantile loss; (2) use a chi2 test to choose the split predictor and search over the splits of that predictor to find the split point. We also propose a tree method that overcomes the problem of crossing quantiles. A cube root rate of convergence of the split point is derived. We illustrate our tree methods with examples on Central America weather data and American infant birthweight data. Comparisons of our methods with some other quantile regression methods are given.;Many statistical applications can be implemented in a parallel way. On a single computer, the parallel computing can be conducted in the CUDA programming model on the graphics processing unit (GPU). We introduce some statistical methods that can be implemented in CUDA. Running the code in CUDA on GPU shows superior computing power compared to running on central processing unit (CPU). In local polynomial example, we gain about 100 times speed up compared to the CPU execution.;Most active effect identification methods for unreplicated factorial design require the sparsity assumption, that only a small fraction of the effects are actually active. The performance of many methods goes down when the number of active effects increases. We propose to combine a normality test statistic and another statistic derived from Dong's method into a step-down testing procedure. This approach does not need to assume sparsity. Our simulation results show that it can obtain consistent performance even when there are a large number of active effects.
机译：我们介绍用于估计分位数的二进制回归树方法。分位数回归树可以捕获分布的不同分位数处的响应和预测变量之间的关系。这些树是通过将预测变量空间递归划分为终端节点并将线性分位数回归模型拟合到终端节点而构建的。我们提供了两个选择分区的选项：（1）在所有预测变量和所有可能的拆分中进行搜索，以选择将最小化分位数损失的预测变量和拆分； （2）使用chi2检验选择分裂预测变量，并搜索该预测变量的分裂以找到分裂点。我们还提出了一种克服交叉分位数问题的树方法。得出分裂点的立方根收敛速率。我们以中美洲天气数据和美国婴儿出生体重数据为例来说明我们的树方法。给出了我们的方法与其他分位数回归方法的比较。;许多统计应用程序可以并行方式实现。在单台计算机上，可以在CUDA编程模型中的图形处理单元（GPU）上进行并行计算。我们介绍了一些可以在CUDA中实现的统计方法。与在中央处理器（CPU）上运行相比，在GPU上的CUDA中运行代码显示出更高的计算能力。在局部多项式示例中，与CPU执行相比，我们的速度提高了约100倍。大多数非复制阶乘设计的主动效果识别方法都需要稀疏假设，即只有很小一部分效果实际上是主动的。当主动效果的数量增加时，许多方法的性能都会下降。我们建议将正态性检验统计量和从Dong方法得出的另一个统计量合并到逐步降低的检验过程中。这种方法不需要假定稀疏性。我们的仿真结果表明，即使存在大量主动效果，它也可以获得一致的性能。

著录项

  • 作者

    Zheng, Wei.;

  • 作者单位

    The University of Wisconsin - Madison.;

  • 授予单位 The University of Wisconsin - Madison.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 129 p.
  • 总页数 129
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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