CAREER: Gaussian Graphical Models: Theory, Computation, and Applications

技术进步和信息时代使得以前所未有的分辨率收集大量数据成为可能。要利用这些数据深入了解复杂现象，就需要描述大量变量之间的关系。图形模型以网络的形式明确地捕捉感兴趣的变量之间的统计关系。这种表示除了增强模型的可解释性外，还可以实现计算效率高的推理。研究者开发了一种方法，从观测数据中推断大量变量之间的无向和有向网络。这项研究具有广泛的社会影响，因为它影响了从天气预报到系统发育和个性化医疗的应用领域。此外，PI是麻省理工学院在统计学方面新聘用的首批教员之一。因此，PI在创建新的统计学本科和博士课程方面具有重大影响，以培养下一代大数据分析能力，这对于在这个数据丰富的世界中承担具有挑战性的角色至关重要。该项目的目标是使用综合方法研究概率图形模型，该方法结合了应用代数几何、凸优化、数理统计和机器学习的思想，并将这些模型应用于科学上重要的新问题。研究议程分为三个项目。在第一个项目中，研究者利用有向高斯图形模型的框架，结合优化和代数几何的工具，开发了从观测数据推断变量之间因果关系的方法。最终目标是应用这种新方法，从基因表达数据（如基因型-组织表达（GTEx）项目）中了解组织和个人特异性基因调控网络。在第二个项目中，研究者开发了可扩展的方法，用于在协方差矩阵或其逆上具有线性约束的高斯模型中的最大似然估计。这些模型对于系统发育树或细胞分化树的推断具有重要意义。第三个项目是将图形模式应用于天气预报；研究人员开发了新的基于高斯copuls的参数方法和考虑天气变量在空间和时间上复杂依赖结构的数值天气预报模型后处理的非参数方法。

Technological advances and the information era allow the collection of massive amounts of data at unprecedented resolution. Making use of this data to gain insight into complex phenomena requires characterizing the relationships among a large number of variables. Graphical models explicitly capture the statistical relationships between the variables of interest in the form of a network. Such a representation, in addition to enhancing interpretability of the model, enables computationally efficient inference. The investigator develops methodology to infer undirected and directed networks between a large number of variables from observational data. This research has broad societal impact, as it affects application domains from weather forecasting to phylogenetics and to personalized medicine. In addition, the PI is one of the initial faculty hires in a new MIT-wide effort in statistics. As such, the PI has major impact on creating new undergraduate and PhD programs in statistics to train the next generation in big data analytics, crucial for taking on challenging roles in this data-rich world.The goal of this project is to study probabilistic graphical models using an integrated approach that combines ideas from applied algebraic geometry, convex optimization, mathematical statistics, and machine learning, and to apply these models to scientifically important novel problems. The research agenda is structured into three projects. In the first project, the investigator develops methods to infer causal relationships between variables from observational data using the framework of directed Gaussian graphical models combined with tools from optimization and algebraic geometry. The end goal is to apply this new methodology to learn tissue- and person-specific gene regulatory networks from gene expression data such as the Genotype-Tissue Expression (GTEx) project. In the second project, the investigator develops scalable methods for maximum likelihood estimation in Gaussian models with linear constraints on the covariance matrix or its inverse. Such models are important for inference of phylogenetic trees or cellular differentiation trees. The third project is an application of graphical models to weather forecasting; the investigator develops new parametric methods based on Gaussian copulas and also non-parametric methods for the post-processing of numerical weather prediction models that take into account the complicated dependence structure of weather variables in space and time.