Mathematical Sciences: "Computer Intensive Methodology in Classification and Regression"

数学科学：“分类和回归中的计算机密集方法”

• 批准号: 9212419
• 负责人: Leo Breiman
• 金额: $ 26.79万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-04-01 至 1997-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9212419&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Computer; Intensive; Methodology

This is a three year research project which has as its purpose the study of computationally intensive methods in classification (pattern recognition) and regression (noisy prediction) where the data is high-dimensional and nonlinear. The research involves new approaches to binary tree structured methods, with the goal of significantly improving on the accuracy and flexiblity of the present, widely used tree structured methods initiated by the book and software presented by Breiman et. al. (1984). The advances in methodology will be useful in the many and diverse areas that make use of classification and prediction. Current areas of interest including speech recognition, image processing, medical diagnosis, and handwritten and printed charactor recognition. There will be five areas of concentration. Two of these are based on recent work by Breiman (1991) for efficiently fitting very high dimensional noisy data by continuously joined hyperplane segments. Similar algorithms will be used to construct trees by fitting hyperplanes in the nodes, and by using multivariate "ramp" functions to construct continuous approximations to prediction surfaces. The other three areas include a promising method for optimizing trees, making them multi-step optimal instead in one- step at present, hyperplane splitting for multiple response trees and a new method for doing penalized linear prediction. This latter method, called Bridge Regression, offers hope of providing uniformly better prediction than ordinary least squares.

这是一个为期三年的研究项目，其目的是研究数据高维和非线性的分类（模式识别）和回归（噪声预测）的计算密集型方法。该研究涉及二叉树结构方法的新方法，其目标是显著提高目前广泛使用的树结构方法的准确性和灵活性，该方法由Breiman et. al.（1984）提出的书籍和软件发起。方法上的进步将在利用分类和预测的许多不同领域发挥作用。当前感兴趣的领域包括语音识别、图像处理、医疗诊断以及手写和打印字符识别。将有五个重点领域。其中两个是基于Breiman（1991）最近的工作，通过连续连接的超平面段有效地拟合非常高维的噪声数据。类似的算法将用于通过拟合节点中的超平面来构建树，并通过使用多元“斜坡”函数来构建预测曲面的连续逼近。其他三个领域包括一种很有前途的优化树的方法，使它们从目前的一步优化到多步优化，多响应树的超平面分裂和一种新的惩罚线性预测方法。后一种方法，称为桥回归，提供了比普通最小二乘更好的预测的希望。