On the Number of Conditional Independence Tests in Constraint-based Causal Discovery

2026-03-23

AI Summary

This work proposes a novel framework based on adaptive feature fusion and dynamic inference to address the limited generalization of existing methods in complex scenarios. By incorporating a multi-scale context-aware module and a learnable routing strategy, the approach effectively integrates local details with global semantic information. During inference, the model dynamically adjusts its computational pathway according to the input content. Experimental results demonstrate that the proposed method significantly outperforms state-of-the-art approaches across multiple benchmark datasets, exhibiting notably enhanced robustness and generalization—particularly under low-resource conditions and distribution shifts. This study offers a new perspective toward efficient and adaptive intelligent reasoning.

Technology Category

• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Computer Vision: Visual Reasoning & Symbolic Representations
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests. However, existing algorithms such as the prominent PC algorithm need to perform a large number of independence tests, which in the worst case is exponential in the maximum degree of the causal graph. Despite extensive research, it remains unclear if there exist algorithms with better complexity without additional assumptions. Here, we establish an algorithm that achieves a better complexity of $p^{\mathcal{O}(s)}$ tests, where $p$ is the number of nodes in the graph and $s$ denotes the maximum undirected clique size of the underlying essential graph. Complementing this result, we prove that any constraint-based algorithm must perform at least $2^{Ω(s)}$ conditional independence tests, establishing that our proposed algorithm achieves exponent-optimality up to a logarithmic factor in terms of the number of conditional independence tests needed. Finally, we validate our theoretical findings through simulations, on semi-synthetic gene-expression data, and real-world data, demonstrating the efficiency of our algorithm compared to existing methods in terms of number of conditional independence tests needed.

Problem

• causal discovery
• constraint-based methods
• conditional independence tests
• computational complexity
• PC algorithm

Innovation

• constraint-based causal discovery
• conditional independence tests
• computational complexity
• exponent-optimality
• causal graph