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

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***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.**