Exact and Monte Carlo Methods for Network Likelihood Estimation

Advisor: Prof. Chenlei Leng, Department of Applied Mathematics, The Hong Kong Polytechnic University

This research develops scalable computational methods for conditional likelihood estimation in directed reciprocal and undirected network formation models. The project addresses the computational and memory costs of exhaustively enumerating informative tetrads in large networks.

Structure-aware exact-search algorithms identify all informative tetrads directly from observed network configurations while reproducing the full conditional likelihood without information loss. Numerical experiments verify their losslessness and improved computational-complexity scaling relative to exhaustive enumeration.

For larger networks, a Direct Monte Carlo method samples from implicitly defined tetrad strata without first storing all informative tetrads. Theoretical analysis and simulation studies establish its statistical properties and demonstrate accurate parameter estimation under limited Monte Carlo budgets. A manuscript based on this research is currently in preparation.