Effective Dimension Reduction for Both Input and Output Variables

这项建议涉及到对多维大数据的分析。由于各种原因，通常希望首先进行降维。利用分片逆回归技术和主海森方向作为积木，发展了适用于同时涉及多个输入和输出变量的更复杂应用的新方法。当变量由时间序列或曲线组成时，自动基函数搜索系统被用来对确定性趋势和随机模式进行建模。来自不同学科的科学数据以前所未有的数量和复杂性积累起来。微阵列技术产生的大量基因表达谱就是例证。隐藏在许多公共可访问的丰富数据库下的是一座生物信息的金矿，等待基因组研究人员的探索。聚类和分类中强大的统计方法被成功地应用于挖掘它们。但可以提炼出的信息种类如此之多，以至于对新途径的追求是理所当然的。本项目开发的新方法将满足这一需求。特别是，它们可以用来可视化基因表达中的局部和全局相互作用，推断代谢回路和酶功能，阐明细胞周期不同阶段的多任务协调，以及探索药物反应性和基因图谱之间的关系。

This proposal is concerned with the analysis of large data with many dimensions. For a variety of reasons, it is often desirable to reduce the dimensionality first. Using the techniques of sliced inverse regression and principal Hessian directions as building blocks, new methods are developed for more complex applications involving many input and output variables simultaneously. When the variables consist of time series or curves, automatic basis searching systems are derived for modeling both the deterministic trends and the stochastic patterns. Scientific data from a variety of disciplines have accumulated in unprecedented volume and complexity. This is exemplified by the massive gene expression profiles generated by microarray technologies. Hidden under many public accessible rich databases is a gold mine of biological messages, awaiting genomic researchers' exploration. Powerful statistical methods from clustering and classification have been successfully applied to dig them out. But the variety of information that can be distilled is so diverse that the pursuit of new paths is more than warranted. The new methods developed in this project will meet this demand. In particular, they can be used to visualize both the local and the global interaction in gene expression, to infer metabolic circuitry and enzyme functionality, to shed light on the multi-task coordination at different stages of the cell cycle, and to explore the relationship between drug responsiveness and gene profiles.