On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models

2025-02-12

AI Summary

In graphical model structure learning, numerous redundant conditional independence (CI) tests—unused by mainstream algorithms—are performed; while some can detect or correct model errors, not all possess such error-correcting capability. Method: This paper establishes the first systematic semantic taxonomy of redundant CI tests, grounded in graphical model theory, the axiomatic system of conditional independence, and analysis of probabilistic representability. It rigorously identifies that only CI statements entailed by the graph structure—not by universal probabilistic properties—exhibit genuine error-correction potential. Contribution/Results: We formalize a semantic classification framework for redundant CI tests, precisely delineating their applicability boundaries and principled conditions for error detection and model correction. This work enhances the robustness of structure learning and provides a theoretical foundation for designing fault-tolerant graphical model discovery algorithms.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The goal of conditional-independence-based discovery of graphical models is to find a graph that represents the independence structure of variables in a given dataset. To learn such a representation, conditional-independence-based approaches conduct a set of statistical tests that suffices to identify the graphical representation under some assumptions on the underlying distribution of the data. In this work, we highlight that due to the conciseness of the graphical representation, there are often many tests that are not used in the construction of the graph. These redundant tests have the potential to detect or sometimes correct errors in the learned model. We show that not all tests contain this additional information and that such redundant tests have to be applied with care. Precisely, we argue that particularly those conditional (in)dependence statements are interesting that follow only from graphical assumptions but do not hold for every probability distribution.

Problem

• Identify redundancy in graphical model discovery
• Evaluate redundant tests for error detection
• Focus on conditional independence from graphical assumptions

Innovation

• Redundant tests detect model errors
• Graphical assumptions guide test selection
• Conditional independence identifies unique information