Embedding learning for complex and heterogeneous networks

Networks play a central role in representing complex relationships among interconnected entities across diverse scientific domains. The increasing scale and complexity of real-world networks often make analytic tasks computationally expensive or intractable. Learning low-dimensional embeddings from high-dimensional and dependent network data has emerged as a powerful strategy, distilling essential structural information into manageable, interpretable, and computationally efficient representations. These embeddings are instrumental in facilitating downstream analyses and enhancing the practical utility of complex networks. In many data-driven scientific inquiries, researchers require not only accurate embedding estimates but also rigorous uncertainty quantification to ensure reliable inference and decision-making. Furthermore, data collected across varying conditions, time periods, or modalities often lead to the prevalence of multiple heterogeneous networks, yielding pressing needs for comparative and integrative analyses. This project will address these vital challenges by developing comprehensive methodologies for the estimation, inference, and integration of network embeddings. Additionally, it will generate broad educational impacts through research training opportunities for graduate and undergraduate students, innovations in curriculum development, and public engagement through outreach activities. This project will advance the statistical foundations of embedding learning for complex and heterogeneous networks through three core objectives. First, it will develop novel methodologies with rigorous theoretical guarantees for estimating and quantifying uncertainty in network embeddings under general models with relaxed assumptions. Second, the project will design statistically principled procedures for comparing network embeddings across distinct conditions, ensuring appropriate handling of inherent variability and effective detection of structural anomalies. Third, the project will construct an innovative framework for jointly analyzing and integrating embeddings from multiple heterogeneous networks. It will leverage the shared information across related but distinct network structures to fully exploit statistical efficiency. Collectively, these contributions will deepen the theoretical understanding of network embedding learning and produce a rigorous yet flexible toolkit that bridges the gap between statistical theory and practical network analysis in real-world applications. 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.