Networks model complex systems in myriad applications, including social media, finance, and political systems. In such settings, nodes often represent people, artificial agents, or political parties while edges portray their relationships. Interpersonal relationships change due to a person’s cognitive biases, societal roles, and what their in-group perceptions are. These relationships impact one's task performance. Often times, there is a need to estimate the underlying relationships and forecast their changes. This dissertation is at the intersection of machine learning, network science, and social science. In our studies, we use graph theory, natural language processing, and convex optimization to extract information on how to improve the performance of individuals in financial and social systems.

First, by leveraging data, we study how the patterns of change in positive and negative relationships may impact the performance of stock traders. We build upon theories from sociology, namely structural balance theory—which describes the dynamics that govern the sentiment of interpersonal relationships—and assess the impact on stock traders' profitability. Our studies show traders trade best when their social network at their workplace is structurally balanced.

Second, we show a generalization of structural balance theory that describes the dynamics of relationships among countries over more than two decades. We capture their dynamics using a time-varying Markov model, pinpoint the international shocks, and international conflicts. We also present rigorous proof for the convergence rate of the proposed model.

Third, we collect data from human subjects answering trivia questions in teams of four. After individually answering a question, subjects collaborate on a final answer through a chat system. The participants are periodically asked to assess their appraisals of each other. We seek to find underlying factors that contribute to the awarded appraisals. We report that expertise and social confidence are the two most salient factors in determining the amount of influence one may receive. Furthermore, we build a model using message content, message times, and individual task performance to estimate the interpersonal influence matrix. Our experimental results demonstrate that the proposed neural network model surpasses baseline algorithms.