Correlated Graphical Models for High-Dimensional Heterogeneous Data: Theory, Optimization, and Applications

该项目的动机是迫切需要分析来自多个来源的现代高维异质数据。在高通量生物技术的推动下，对同一组对象进行多种类型的测量越来越常见。集成不同类型的数据是获得有关生物过程的基础知识的关键。现代生物数据的复杂特性也给数据分析和统计建模带来了挑战。该项目将通过适用于融合来自静态和动态条件的相关和混合数据的新的图形模型来促进理论和方法的发展。这些方法在将丰富的数据转化为有意义的知识方面具有巨大的潜力。新的统计方法和理论也将推动现代统计科学的发展。该项目的成果将为科学界提供有价值的软件工具。本研究将促进课程开发、学生培养和教育拓展。不同实验平台的多模式数据具有不同的属性和特点。在许多系统中，包括生物过程，调节本质上是模块化的和时间动态的。共同的调控原则存在于某些相关的生物条件中。该项目将侧重于开发新的数据集成方法和理论，从频率推理的角度通过新的相关图形模型进行开发。这些方法将基于指数马尔可夫随机场，而不是传统的高斯假设。新方法将允许从多个静态和动态条件下对高维异质数据进行网络发现。该项目还涉及开发用于复杂优化问题的高效算法，其中包括结构诱导正则化机制。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project is motivated by the pressing need for analyzing modern high-dimensional heterogeneous data from multiple sources. Driven by high-throughput biotechnologies, it is increasingly common to have multiple types of measurements on the same set of subjects. Integration of heterogeneous data types is the key to gaining fundamental knowledge on biological processes. Complex characteristics of modern biological data also result in challenges for data analysis and statistical modeling. This project will contribute to theoretical and methodological development through novel graphical models suitable for fusing correlated and mixed data from static and dynamic conditions. These approaches have great potential to translate rich data into meaningful knowledge. The new statistical methods and theories will also advance modern statistical science. The resulting products of this project will provide valuable software tools to scientific communities. This research will promote curriculum development, student training, and educational outreach.Multimodal data from different experimental platforms have different properties and characteristics. In many systems, including biological processes, regulation is modularized and temporally dynamic in nature. Common regulatory principles exist in certain related biological conditions. This project will focus on the development of new data integration methods and theories through novel correlated graphical models from a frequentist inference perspective. The methods will be based on exponential Markov random fields beyond the traditional Gaussian assumption. The new methods will allow for network discovery for high-dimensional heterogeneous data from multiple static and dynamic conditions. This project also involves the development of efficient algorithms for complex optimization problems incorporating the structure-inducing regularization mechanism.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.