From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables

2026-04-24

AI Summary

This work addresses the significant challenge of causal discovery in the presence of latent variables and without assuming causal sufficiency. Existing approaches often lack a global perspective or rely on predefined variable clusters, limiting their applicability. To overcome these limitations, we propose L2C, a unified end-to-end framework that simultaneously performs clustering and causal discovery without requiring prior knowledge of clusters or the causal sufficiency assumption. L2C integrates local causal structure learning with cluster-level reasoning and leverages a cluster reduction theorem to automatically identify variable clusters while preserving full causal information, thereby constructing a cluster-level causal graph. Experimental results demonstrate that L2C accurately recovers ground-truth clusters on both synthetic and real-world datasets and substantially outperforms existing baselines in identifying macro-level causal effects.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Latent variables pose a fundamental challenge to causal discovery and inference. Conventional local methods focus on direct neighbors but fail to provide macro level insights. Cluster level methods enable macro causal reasoning but either assume clusters are known a priori or require causal sufficiency. Moreover, directly applying single variable causal discovery methods to cluster level problems violates causal sufficiency and leads to incorrect results. To overcome these limitations, this paper proposes L2C (Local to Cluster Causal Abstraction), a unified framework that bridges local structure learning and cluster level causal discovery. Unlike prior work that requires a complete manual assignment of micro variables to clusters, L2C discovers the partition automatically from local causal patterns. Our solution leverages a cluster reduction theorem to reduce any cluster to at most three nodes without loss of causal information, applies local causal discovery to identify direct causes, effects, and V structures in the presence of latent variables, and performs macro level causal inference via cluster level calculus on the learned cluster graph. L2C does not assume causal sufficiency, as latent variables are handled through local discovery. Theoretical analysis shows that L2C ensures soundness, atomic completeness, and computational efficiency. Extensive experiments on synthetic and real world data demonstrate that L2C accurately recovers ground truth clusters and achieves superior macro causal effect identification compared to existing baselines.

Problem

• causal discovery
• latent variables
• cluster-level causality
• causal sufficiency
• macro causal reasoning

Innovation

• causal discovery
• latent variables
• cluster abstraction
• causal sufficiency
• local-to-global inference