Artificial Intelligence and Network Science: Solution Concepts, Graph-Theoretic Characterizations, and Their Societal Aspects

计算方法和计算技术已被广泛用于解决具有科学和社会意义的问题。虽然基于这些技术的软件系统是用创新的想法设计的(通常是在复杂的数学框架下)，以提高效率和最好地利用现有数据，但解释这些系统产生的解决方案的含义并证明其合理性已变得越来越具有挑战性。众所周知，网络科学在划定网络社区以及人工智能(AI)处理公平或其他社会问题方面缺乏原则性的方法。我同意这样一种建议，即理解这些系统和基本方法需要“概念和方法范式的转变”，我认为关键在于开发能够捕捉问题和潜在现象的内在特征的解决方案概念。为了服务于我的长期目标，即为人工智能、网络科学及相关领域的问题开发数学合理、计算高效、对社会负责的计算方法和建模工具，拟议的五年计划旨在通过专注于现有解决方案概念的图论、概率和算法表征以及设计可直接使用或可在实践中作为参考的新解决方案概念来应对这一挑战。利用计算机科学、图论和概率论的工具，研究将沿着三条线进行，涉及(I)解决方案概念，这些解决方案概念概括、放松或专门化人工智能推理、算法决策和网络分析中的问题的标准解决方案概念；(Ii)复杂网络的社区结构和其他中尺度组织，特别是那些从网络实体的高阶交互中出现的、可以以图论性质或功能/社会约束为特征的组织；以及(Iii)具有特殊性质的子图，可以用作与网络上的动态过程相关的问题的解决方案概念。这项研究有望显著提高我们对人工智能推理、算法决策和网络分析中几类重要问题的计算和社会方面的知识。它在数据丰富的领域具有实际意义，在这些领域，计算和网络视角已经变得不可或缺。我们对解决方案概念的描述将提供一个独特的视角，以帮助实现开发高效和健壮的推理、学习和数据分析系统的目标，这些系统与人类的社会和伦理价值观很好地一致。通过研究开发的算法思想和数学模型可以被研究人员/从业者用来开发软件系统，以分析生物学、经济学、医疗保健、社交媒体和社会学中的复杂现象。

Computational approaches and computing techniques have been widely used to solve problems of scientific and societal significance. While software systems based on these techniques are designed with innovative ideas (and often under complicated mathematical frameworks) in order to improve efficiency and to make best use of available data, it has become increasingly challenging to interpret the meaning of the solutions produced by these systems and to justify their rationale. It is well recognized that principled approaches are lacking in Network Science to delineating network communities and in Artificial Intelligence (AI) to dealing with fairness or other societal issues. I concur with the suggestion that understanding these systems and the underlying methods requires "conceptual and methodological paradigm shifts", and I believe that the key lies in developing solution concepts that capture the intrinsic characteristics of the problems and the underlying phenomena. To serve my long-term goal of developing mathematically sound, computationally efficient, and socially responsible computing methods and modelling tools for problems in AI, Network Science, and related domains, the proposed five-year program aims to address the challenge by focusing on the graph-theoretic, probabilistic, and algorithmic characterizations of existing solution concepts and the design of new solution concepts that can be used directly or as a reference in practice. Using tools from computer science, graph theory, and theory of probability, the research will be carried out along three lines of inquiry, dealing with (I) solution concepts that generalize, relax, or specialize standard solution concepts for problems in AI reasoning, algorithmic decision making, and network analysis; (II) community structure and other meso-scale organizations of complex networks, in particular, those that emerge from higher-order interactions of network entities and can be characterized by graph-theoretic properties or functional/societal constraints; and (III) subgraphs with special properties that can be used as a solution concept for problems related to dynamic processes on networks. The research is expected to significantly advance our knowledge on the computational and societal aspects of several classes of important problems in AI reasoning, algorithmic decision making, and network analysis. It has practical implications in data-rich domains where computational and network perspectives have become indispensable. Our characterizations of solution concepts will provide a unique perspective to help achieve the goal of developing efficient and robust reasoning, learning, and data analysis systems that align well with humans' social and ethic values.  Algorithmic ideas and mathematical models developed through the research can be used by researchers/practitioners to develop software systems to analyze complex phenomena in biology, economics, healthcare, social media, and sociology.