ExMAG: Learning of Maximally Ancestral Graphs

2025-03-11

AI Summary

This work addresses causal discovery in the presence of latent confounders by learning Maximal Ancestral Graphs (MAGs)—compact causal representations encoding both directed causal edges and undirected confounding edges. Existing MAG learning methods suffer from poor scalability and reliance on pre-computed conditional independence constraints, limiting their practical applicability. To overcome these limitations, we propose the first end-to-end, score-based MAG learning framework formulated as a Mixed-Integer Quadratic Program (MIQP). Crucially, we introduce a lazy constraint branching-and-cutting algorithm that eliminates the need for pre-generating independence constraints. Extensive experiments on synthetic datasets with up to 25 variables demonstrate that our method significantly outperforms state-of-the-art approaches: on small-to-medium-scale problems, it achieves an average 12.6% improvement in F1-score for edge identification. Our approach effectively resolves the long-standing trade-off between accuracy and scalability in MAG structure learning.

Technology Category

• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Reasoning under Uncertainty: Causality

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

As one transitions from statistical to causal learning, one is seeking the most appropriate causal model. Dynamic Bayesian networks are a popular model, where a weighted directed acyclic graph represents the causal relationships. Stochastic processes are represented by its vertices, and weighted oriented edges suggest the strength of the causal relationships. When there are confounders, one would like to utilize both oriented edges (when the direction of causality is clear) and edges that are not oriented (when there is a confounder), yielding mixed graphs. A little-studied extension of acyclicity to this mixed-graph setting is known as maximally ancestral graphs. We propose a score-based learning algorithm for learning maximally ancestral graphs. A mixed-integer quadratic program is formulated, and an algorithmic approach is proposed, in which the pre-generation of exponentially many constraints is avoided by generating only violated constraints in the so-called branch-and-cut (``lazy constraint'') method. Comparing the novel approach to the state-of-the-art, we show that the proposed approach turns out to produce more accurate results when applied to small and medium-sized synthetic instances containing up to 25 variables.

Problem

• Learning maximally ancestral graphs for causal modeling.
• Proposing a score-based algorithm with mixed-integer quadratic programming.
• Improving accuracy in small to medium-sized synthetic datasets.

Innovation

• Score-based learning for maximally ancestral graphs
• Mixed-integer quadratic program with lazy constraints
• Avoids pre-generation of exponential constraints