Effective Dimension Reduction for Both Input and Output Variables

这一建议涉及对具有多个维度的大数据的分析。由于各种原因，通常需要先降低维数。利用切片逆回归技术和主要Hessian方向作为构建块，开发了涉及多个输入和输出变量同时的更复杂应用的新方法。当变量由时间序列或曲线组成时，导出了自动基搜索系统，用于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。隐藏在许多可公开访问的丰富数据库之下的是一个生物信息的金矿，等待着基因组研究人员的探索。从聚类和分类的强大统计方法已经成功地挖掘出来。但是，可以提取的信息种类是如此之多，以至于寻求新的途径是有必要的。本项目开发的新方法将满足这一需求。特别是，它们可以用于可视化基因表达的局部和全局相互作用，推断代谢回路和酶功能，揭示细胞周期不同阶段的多任务协调，并探索药物反应性和基因谱之间的关系。

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.