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

这个项目的动机是迫切需要分析现代高维异构数据从多个来源。在高通量生物技术的推动下，对同一组受试者进行多种类型的测量越来越普遍。异构数据类型的集成是获得生物过程基础知识的关键。现代生物数据的复杂特征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静态和动态条件下相关和混合数据的新型图形模型，促进理论和方法的发展。这些方法具有将丰富的数据转化为有意义的知识的巨大潜力。新的统计方法和理论也将推动现代统计科学的发展。该项目的最终产品将为科学界提供宝贵的软件工具。不同实验平台的多模态数据具有不同的性质和特点。在许多系统中，包括生物过程，调节是模块化的，本质上是时间动态的。在某些相关的生物条件下存在共同的调节原则。这个项目将集中在新的数据集成方法和理论的发展，通过新的相关图形模型从频率论推理的角度。该方法将基于指数马尔可夫随机场超越传统的高斯假设。新方法将允许从多个静态和动态条件下的高维异构数据的网络发现。该项目还涉及复杂优化问题的高效算法的开发，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知识价值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.