Addressing pitfalls in implicit unobserved confounding synthesis using explicit block hierarchical ancestral sampling

2025-03-12

AI Summary

Existing causal discovery evaluation suffers from data synthesis bias due to unobserved confounding, as conventional implicit parameterization methods are constrained by diagonal dominance requirements and bidirectional edge restrictions, limiting coverage of the causal model space. Method: We propose a novel paradigm based on explicit block-level ancestral sampling. This involves constructing block-level ancestral graphs, deterministically converting DAGs to ancestral graphs, generating positive-definite covariance matrices, and spectrally controlling partial correlation matrices to ensure unbiased causal model sampling. Contribution/Results: We formally prove that explicit block-level ancestral sampling fully subsumes the model space achievable by implicit methods while overcoming their structural limitations. Empirical evaluation demonstrates substantial improvements in model coverage and assessment robustness across standard benchmarks. Our approach provides a more reliable foundation for evaluating causal discovery and inference algorithms.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• 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

Abstract

Unbiased data synthesis is crucial for evaluating causal discovery algorithms in the presence of unobserved confounding, given the scarcity of real-world datasets. A common approach, implicit parameterization, encodes unobserved confounding by modifying the off-diagonal entries of the idiosyncratic covariance matrix while preserving positive definiteness. Within this approach, state-of-the-art protocols have two distinct issues that hinder unbiased sampling from the complete space of causal models: first, the use of diagonally dominant constructions, which restrict the spectrum of partial correlation matrices; and second, the restriction of possible graphical structures when sampling bidirected edges, unnecessarily ruling out valid causal models. To address these limitations, we propose an improved explicit modeling approach for unobserved confounding, leveraging block-hierarchical ancestral generation of ground truth causal graphs. Algorithms for converting the ground truth DAG into ancestral graph is provided so that the output of causal discovery algorithms could be compared with. We prove that our approach fully covers the space of causal models, including those generated by the implicit parameterization, thus enabling more robust evaluation of methods for causal discovery and inference.

Problem

• Addresses limitations in unbiased sampling of causal models.
• Improves modeling of unobserved confounding in causal discovery.
• Enables robust evaluation of causal discovery algorithms.

Innovation

• Explicit block-hierarchical ancestral sampling
• Converts ground truth DAG to ancestral graph
• Covers full space of causal models