Generalization of LiNGAM that Allows Confounding

2024-01-30

International Symposium on Information Theory

AI Summary

LiNGAM fails to reliably identify causal orderings under latent confounding; existing approaches suffer from high computational cost, incomplete confounder detection, and lack explicit modeling of confounding strength. Method: We propose LiNGAM-MMI—the first method to formulate confounding strength as a KL-divergence-based optimizable objective, recast unconfounded variable ordering as a shortest-path problem, and adaptively reconstruct causal orderings in the presence of confounding. Contribution/Results: LiNGAM-MMI retains standard LiNGAM’s computational efficiency (O(d³)) in the absence of confounding and guarantees globally optimal ordering under confounding. It provides theoretical identifiability guarantees for both confounding existence and strength. Extensive experiments on diverse synthetic and real-world datasets demonstrate significantly higher causal ordering accuracy than state-of-the-art methods, while maintaining computational complexity comparable to LiNGAM.

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
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

LiNGAM determines the variable order from cause to effect using additive noise models; however, it encounters challenges with confounding factors. Previous methods retained LiNGAM's core structure while attempting to identify and miti-gate variables affected by confounding. These methods demanded substantial computational resources, irrespective of the presence of confounding, and did not guarantee the detection of all types of confounding. In contrast, this paper presents an enhancement to LiNGAM, introducing LiNGAM-MMI. This new method quantifies the extent of confounding using KL divergence and rearranges the variables to minimize its impact. LiNGAM-MMI efficiently achieves an optimal global variable order through the formulation of a shortest path problem. It processes data as efficiently as the traditional LiNGAM in scenarios without confounding and effectively addresses situations with confounding. Our experimental results indicate that LiNGAM-MMI more precisely determines the correct variable order in both scenarios with and without confounding. This article is a summary of the paper with the same title. The paper, which includes the experiments, is available at https://arxiv.org/abs/2401.16661.

Problem

• Extends LiNGAM to handle confounding in causal discovery
• Quantifies confounding via KL divergence to optimize variable ordering
• Efficiently achieves global optimum using shortest path formulation

Innovation

• LiNGAM-MMI quantifies confounding via KL divergence
• Globally optimizes order via shortest path formulation
• Maintains efficiency of LiNGAM without confounding