Evaluating the Use of Pseudo-Likelihood Estimation in Complex Dependency Models and Network Structures

Posted: Feb 20, 2015

• Connor Edwards
• Daniel Wood
• Eleanor Butler

Abstract

The analysis of complex dependency structures represents one of the most challenging frontiers in statistical learning and network science. Traditional maximum likelihood estimation methods, while statistically efficient, often become computationally prohibitive when dealing with intricate dependency models, particularly in high-dimensional settings where the normalization constant involves intractable sums over exponentially many configurations. This computational bottleneck has motivated the development of alternative estimation strategies that balance statistical efficiency with computational feasibility. Pseudo-likelihood estimation, first introduced by Besag in the context of spatial statistics, offers a promising alternative by replacing the joint likelihood with a product of conditional probabilities. While this approach has been successfully applied to various Markov random field models, its performance in complex network structures with heterogeneous dependency patterns remains inadequately explored. Existing literature has primarily focused on regular lattice structures or homogeneous networks, leaving a significant gap in understanding how pseudo-likelihood methods perform in realistic network settings characterized by scale-free topologies, community structures, and varying dependency strengths. This research addresses several fundamental questions that have received limited attention in the literature. How does the performance of pseudo-likelihood estimation vary with network topology and dependency structure complexity? What are the theoretical limits of consistency for pseudo-likelihood methods in networks exhibiting power-law degree distributions? Can adaptive weighting schemes improve estimation accuracy while maintaining computational tractability? Our work provides comprehensive answers to these questions through both theoretical analysis and extensive empirical evaluation. The novelty of our approach lies in the development of an adaptive pseudo-likelihood framework that dynamically adjusts to local network characteristics. Unlike conventional methods that treat all conditional dependencies equally, our approach recognizes that the information content varies across different parts of the network.