Near-Optimal Experiment Design in Linear non-Gaussian Cyclic Models

2025-09-25

AI Summary

This work addresses causal graph identification in linear non-Gaussian structural equation models with cycles, leveraging both observational and interventional data. Since observational data alone only identifies the causal graph up to a permutation equivalence class, targeted interventions are required to break this ambiguity. To this end, we propose a compact representation of the equivalence class via bipartite perfect matching, circumventing explicit enumeration of all equivalent graphs. We further design an adaptive stochastic optimization framework for intervention selection, the first to formulate intervention-effect evaluation as a sampling-based estimation—bypassing full-graph enumeration—and prove that its reward function exhibits adaptive submodularity. Experiments demonstrate that our method efficiently recovers the true causal structure with only a small number of interventions, achieving performance close to that of optimal experimental design.

Technology Category

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

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
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study the problem of causal structure learning from a combination of observational and interventional data generated by a linear non-Gaussian structural equation model that might contain cycles. Recent results show that using mere observational data identifies the causal graph only up to a permutation-equivalence class. We obtain a combinatorial characterization of this class by showing that each graph in an equivalence class corresponds to a perfect matching in a bipartite graph. This bipartite representation allows us to analyze how interventions modify or constrain the matchings. Specifically, we show that each atomic intervention reveals one edge of the true matching and eliminates all incompatible causal graphs. Consequently, we formalize the optimal experiment design task as an adaptive stochastic optimization problem over the set of equivalence classes with a natural reward function that quantifies how many graphs are eliminated from the equivalence class by an intervention. We show that this reward function is adaptive submodular and provide a greedy policy with a provable near-optimal performance guarantee. A key technical challenge is to efficiently estimate the reward function without having to explicitly enumerate all the graphs in the equivalence class. We propose a sampling-based estimator using random matchings and analyze its bias and concentration behavior. Our simulation results show that performing a small number of interventions guided by our stochastic optimization framework recovers the true underlying causal structure.

Problem

• Characterizing causal graph equivalence classes in cyclic linear non-Gaussian models
• Designing optimal interventions to identify true causal structure efficiently
• Developing sampling methods to estimate intervention rewards without enumeration

Innovation

• Bipartite graph matching represents causal equivalence classes
• Adaptive submodular optimization designs near-optimal interventions
• Random matching sampling estimates reward without enumeration