CAREER: Theoretical Foundations for Learning Network Dynamics

在相互联系的实体的复杂网络上的动态过程作为物理、生物、工程、社会和经济系统的模型比比皆是。从数据中学习灵活的、人类可解释的这些过程的统计模型是预测和控制这些过程的重要先决条件。设计机器学习模型和算法，即使在非网络环境中，也不能完全从数学上理解。流程的网络化特性给模型的准确性、人类的可解释性和效率带来了额外的挑战。该项目寻求一种新的数学框架、有效的算法和理论保证，以学习复杂网络上进化过程的数据驱动模型。它还旨在为学习模型的验证和解释提供严格的技术。这些进步将提高模型的有效性、准确性、效率和可解释性，适用于各种具有社会影响的应用领域，如流行病学、社会网络上的错误信息传播、电力网络、供应链网络和农业中的营养扩散过程。该项目还包括对代表性不足的博士生、本科生和高中生进行指导；调查员家庭部门理论课程的拓展与农业领域专家合作；还有一个关于机器学习和网络动力学统计的训练营。研究者的目标是一个全面的数学框架学习动态图，从概率，随机图，信息和学习理论绘图。它将讨论统计（样本复杂性）和学习算法和模型的计算效率，现有和新模型类的表达能力，以及模型验证，选择和解释。在整个过程中，图形结构参数对性能的影响将与数学严谨的研究。阐明经典学习规则的局限性，设计出具有理论保障的新型学习规则。将给出新的和经典的基于神经网络的动态模型类的定量通用逼近保证。将设计新的基于交叉验证的算法，为模型验证和选择提供可证明的保证。对模型的可解释性至关重要的一致地真值模型参数估计准则将被制定。这将为数据驱动的网络动态模型的学习、验证和解释提供理论支持的管道。该奖项反映了美国国家科学基金会的法定使命，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。

Dynamic processes on complex networks of interconnected entities abound as models of physical, biological, engineered, social, and economic systems. Learning flexible, human-interpretable statistical models of these processes from data is a vital prerequisite for their prediction and control. Designing machine learning models and algorithms, even in a non-networked setting, is not fully understood mathematically. The networked nature of the processes brings additional challenges for model accuracy, human interpretability, and efficiency. This project seeks a new mathematical framework, efficient algorithms, and theoretical guarantees for learning data-driven models of evolving processes on complex networks. It aims also to provide rigorous techniques for validation and interpretation of learned models. These advances should result in improved model validation, accuracy, efficiency, and interpretability for diverse, societally impactful application domains such as epidemiology, misinformation spread on social networks, electrical power networks, supply chain networks, and nutrient diffusion processes in agriculture. The project additionally involves mentoring of underrepresented doctoral, undergraduate, and high school students; expansion of the investigator's home department's theory curriculum; collaboration with domain experts in agriculture; and a bootcamp on machine learning and statistics for network dynamics.The investigator targets a comprehensive mathematical framework for learning of dynamics on graphs, drawing from probability, random graphs, and information and learning theory. It will address statistical (sample complexity) and computational efficiency of learning algorithms and models, expressive power of existing and novel model classes, and model validation, selection, and interpretation. Throughout, the impact of graph structural parameters on performance will be studied with mathematical rigor. The limitations of classical learning rules will be elucidated, and novel learning rules with theoretical guarantees will be devised. Quantitative universal approximation guarantees for new and classical neural network-based dynamic model classes will be given. Novel cross-validation-based algorithms with provable guarantees for model validation and selection will be devised. Criteria for consistent ground-truth model parameter estimation, important for interpretability of models, will be formulated. This will enable a theoretically-backed pipeline for learning, validation, and interpretation of data-driven network dynamics models.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.