Mining structured tensor data

使用约束似然方法处理包含张量的多元数据的结构化建模情况，作为利用低维结构进行高阶分析的有效手段。例如，在基因网络分析中，约束方法有助于在多个图形模型的背景下揭示基因-基因关系。特别注意适当选择约束以适应各种结构。拟议项目的总体主题是发展在预测和估计方面具有实际效用的统计方法。特别是，拟议的项目开发了以下方法：(a)用于结构提取的多个图形模型，以及(b)张量数据的高阶分析。提出的研究主要是由基因网络分析和协同过滤中出现的挑战性问题所驱动的，其中一个中心问题是如何在发现过程中利用低维结构来对抗高统计不确定性。新技术的提出和研究，计算和统计，针对生物医学和工程问题。在(a)和(b)中，我们的工作将集中在分类和回归，以及通过张量分解和因子分解进行结构适应，其中大部分工作将集中在特定条件下提取低维结构。现代科学和工程研究，如生物医学研究和计算机视觉，现在产生了大量的数据，旨在同时探索成百上千个相互作用单位之间的关系。本项目提出了处理新的科学环境的方法。该项目开发的技术直接适用于应用研究，特别是在自动机器加工和数据挖掘、生物医学研究、广告和经济学方面。此外，还描述了技术转让计划，以及培训学生统计学习和数据挖掘的教育计划。教育活动包括开发一门课程，吸引本科生进行研究。

Structured modeling situations, with multivariate data involving tensors, are treated using constrained likelihood approaches, as an efficient means to exploit lower-dimensional structure for high-order analysis. In gene network analysis, for example, a constrained approach helps reveal gene-gene relations in a context of multiple graphical models. Special attention is devoted to the appropriate choice of the constraints for adaptation to a variety of structures. The general theme of the proposed project is the development of statistical methods of practical utility, both in prediction and estimation. In particular, the proposed project develops methods for (a) multiple graphical models for structure extraction, and for (b) high-order analysis of tensor data. The proposed research is primarily motivated by challenging problems that arise in gene network analysis and collaborative filtering, where one central issue is how to leverage and utilize lower-dimensional structure to battle high statistical uncertainty in a discovery process. New techniques are proposed and investigated, both computationally and statistically, which target biomedical and engineering problems. In (a) and (b), our effort will be on classification and regression, and on structure adaptation through tensor decomposition and factorization, with most effort focused towards condition specific extraction of lower-dimensional structure.Modern scientific and engineering investigation, as in biomedical research and computer vision, now produces enormous data that aim to simultaneously explore relations among hundreds and thousands interacting units. This project proposes methods for treating the new scientific environment. The project develops technology that is directly applicable to applied research, particularly in automatic machine processing and data mining, biomedical research, advertisement, and economics. Plans for technology transfer are described, in addition to an educational program that will train students in statistical learning and data mining. Educational activities include developing a course, and attracting undergraduate students to research.