Tree-Structured Methods for Prediction and Data Visualization

用于预测和数据可视化的树结构方法

• 批准号: 0402470
• 负责人: Wei-Yin Loh
• 金额: $ 24.05万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2008-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0402470&HistoricalAwards=false
• 关键词: Tree; Structured; Methods; Prediction; Data

Though many recursive partitioning algorithms exist in the literature, most are unsuitable for model interpretation because they tend to select some types of predictor variables more frequently than others. As a result, such tree structures can yield misleading conclusions about the roles and relative importance of the predictor variables. The main thrust of the proposed research is to extend the investigator's GUIDE and QUEST strategies to regression and classification, respectively. This approach effectively solves the problem of selection bias and significantly reduces computation time. The computational savings make it feasible to build tree-structured models that are hitherto impractical to construct. A second objective is to use the methods to model unreplicated and fractionally replicated data from designed experiments. The hierarchical structure of tree-structured models and their variable selection ability make them attractive alternatives to traditional methods. A third objective is extension of the investigator's LOTUS algorithm to fit logistic regression trees to data with multinomial response variables. Statistical models constructed from high-dimensional data are often difficult or unintuitive to interpret. This applies even to the simplest model, the multiple linear regression model, where interpretation of the parameter estimates is fraught with difficulties caused by nonlinearity, multicollinearity, and interactions in the data. Graphical visualization is perhaps the most effective way to interpret a model. But such techniques are inapplicable to more than two or three dimensions. The proposed research enables the application of visualization techniques to high-dimensional data by using a tree-structured method to partition the data space such that at most one, two, or three predictor variables are needed to model the data in each partition. The result is a graphical model whose broad features are representable by a tree structure and whose finer features are visualizable by two and three-dimensional graphical displays.

虽然许多递归分割算法存在于文献中，大多数是不适合的模型解释，因为他们往往选择某些类型的预测变量比其他更频繁。因此，这样的树结构可能会产生关于预测变量的作用和相对重要性的误导性结论。建议的研究的主旨是扩展调查员的指南和查询策略，分别回归和分类。这种方法有效地解决了选择偏差的问题，并大大减少了计算时间。计算的节省使得建立迄今为止不切实际的树结构模型成为可能。第二个目标是使用的方法来模拟未复制和部分复制的数据从设计的实验。树结构模型的层次结构和它们的变量选择能力使它们成为传统方法的有吸引力的替代品。第三个目标是扩展研究者的LOTUS算法，以将逻辑回归树拟合到具有多项响应变量的数据。从高维数据构建的统计模型通常难以解释或不直观。这甚至适用于最简单的模型，多元线性回归模型，其中参数估计的解释充满了由数据中的非线性，多重共线性和相互作用引起的困难。图形可视化可能是解释模型的最有效方法。但这种技术不适用于二维或三维以上的空间。所提出的研究，使可视化技术的应用程序，高维数据，通过使用树结构的方法来划分数据空间，这样，最多需要一个，两个或三个预测变量来模拟每个分区中的数据。其结果是一个图形模型，其广泛的功能是由树结构表示，其更精细的功能是可视化的二维和三维图形显示。