Evaluating the Use of Graphical Models in Representing Conditional Dependencies Across Complex Data Systems

Posted: Jan 01, 2023

• Hunter Barnes
• Jasmine Reed
• Jeremy Cox

Abstract

The representation of conditional dependencies in complex data systems represents one of the most challenging problems in contemporary data science. As datasets grow in both dimensionality and heterogeneity, traditional statistical methods struggle to capture the intricate web of relationships that characterize modern data ecosystems. Graphical models have long served as a foundational tool for representing conditional dependencies, yet their application to increasingly complex systems has revealed significant limitations in scalability, interpretability, and representational capacity. This research addresses these challenges through a novel evaluation framework that extends graphical modeling beyond its conventional boundaries. Complex data systems, characterized by high dimensionality, heterogeneous data types, and multi-scale structures, present unique challenges for dependency analysis. Traditional graphical models, while theoretically sound, often fail to capture the hierarchical and emergent dependency patterns that characterize such systems. The fundamental research question driving this investigation concerns how graphical models can be adapted and extended to effectively represent conditional dependencies in data environments where traditional assumptions of independence and stationarity no longer hold. Our contribution lies in developing and validating a hybrid framework that integrates probabilistic graphical models with topological data analysis, creating a multi-scale approach to dependency representation. This integration enables the identification of dependency structures that operate across different levels of data granularity, from fine-grained pairwise relationships to coarse-grained systemic dependencies. The framework represents a significant departure from conventional approaches by explicitly modeling how dependency structures evolve across scales and contexts.