Estimation, inference and testing for large-scale directed network models

大规模交互网络自然而然地出现在许多现代科学应用中。例如，在生物化学和系统生物学中，蛋白质序列中不同位置的氨基酸相互作用，而在计算神经科学中，大脑中神经元之间的连接网络自然会触发对特定刺激的反应。该项目将开发可靠和可扩展的算法，用于学习许多节点之间的底层交互网络。由于上述应用中的规模、复杂性和不断变化的数据技术，本项目中解决的挑战将导致新理论和方法的发展，以及应用领域新算法的实施。该项目的目标是解决大规模网络模型的估计、推理和测试的挑战。考虑到所产生的网络的规模，这个项目提出了一些计算和统计挑战，PI将通过集中于两种方法来解决：(1)多变量时间序列模型；(2)有向图形模型。PI的前期工作为大规模非线性时间序列模型和有向图形模型发展了新的理论和方法。这项先前的工作指出了本项目将对这两种方法提出的许多重大开放挑战。这些挑战包括：(I)缺乏学习复杂依赖结构的样本量/统计资源；(Ii)由于依赖模型的非凸性和大搜索空间而带来的计算挑战；(Iii)将领域知识和科学实验纳入估计方法；以及(Iv)利用学习的网络进行假设检验、推理和参数估计。该项目将应对这些挑战，这些贡献将导致网络学习新方法的开发。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。

Large-scale interaction networks naturally arise in many modern scientific applications. For example, in biochemistry and systems biology, amino acids in different locations of the protein sequence interact, while in computational neuroscience, connectivity networks amongst neurons in the brain naturally trigger responses to particular stimuli. This project will develop reliable and scalable algorithms for learning the underlying interaction network amongst many nodes. Due to both the scale, complexity, and the changing data technologies in the applications described above, the solutions to the challenges addressed in this project will lead both to the development of novel theory and methodology, and the implementation of new algorithms for the application domains. The goal of the project is to address the challenge of estimation, inference and testing for large-scale network models. Given the size of the networks generated, this project presents a number of computational and statistical challenges the PI will address by focusing on two methodologies: (i) multivariate time series models; (ii) directed graphical models. The PI's prior work has developed new theory and methodology both for large-scale non-linear time series models and directed graphical models. This prior work points to a number of significant open challenges for both methodologies that this project will. These challenges include: (i) lack of sample size/statistical resources for learning complicated dependence structures; (ii) computational challenges due to non-convexity and large search-spaces for dependence models; (iii) incorporating domain knowledge and scientific experiments into the estimation methodologies; and (iv) exploiting learned networks for hypothesis testing, inference, and parameter estimation. This project will address these challenges and these contributions will lead to the development of new methods for network learning.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.