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

这是一个为期三年的研究项目，其目的是研究分类(模式识别)和回归(噪声预测)中的计算密集型方法，其中数据是高维和非线性的。这项研究涉及二叉树结构方法的新方法，目的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，这些方法是由Breiman et提出的书和软件发起的。艾尔(1984)。方法论上的进步将在利用分类和预测的许多不同领域中发挥作用。目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印刷体字符识别。将有五个集中领域。其中两个是基于Breiman(1991)最近的工作，该工作通过连续连接的超平面分段来有效地拟合高维噪声数据。类似的算法将被用来构建树，方法是在节点中拟合超平面，并使用多变量的“斜坡”函数来构建对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，使它们目前在一步中实现多步最优，多响应树的超平面分裂，以及进行惩罚线性预测的新方法。后一种方法被称为桥回归，它提供了比普通最小二乘法一致更好的预测。

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.