Toward Scalable and Valid Conditional Independence Testing with Spectral Representations

2025-12-22

AI Summary

Conditional independence (CI) testing is fundamental to causal inference and graphical modeling, yet conventional methods often rely on restrictive structural assumptions, limiting practical performance. While kernel-based partial covariance operator approaches offer greater principled grounding, they suffer from poor adaptivity, slow convergence, and limited scalability. This paper introduces a learnable representation framework grounded in spectral decomposition of the partial covariance operator—marking the first deep integration of spectral representation learning with CI testing. We establish a theoretical mapping from representation error to statistical power and propose a two-level contrastive learning algorithm that ensures statistical validity while enhancing computational efficiency. We prove asymptotic validity and controllable power for the resulting test. Experiments demonstrate that our method significantly outperforms existing kernel-based approaches on high-dimensional real-world data, achieving superior robustness, scalability, and statistical reliability.

Technology Category

• Machine Learning: Causal Learning
• Computer Vision: Representation Learning for Vision
• Reasoning under Uncertainty: Causality

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity on real-world data. Kernel methods using the partial covariance operator offer a more principled approach but suffer from limited adaptivity, slow convergence, and poor scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of the partial covariance operator and use them to construct a simple test statistic, reminiscent of the Hilbert-Schmidt Independence Criterion (HSIC). We also introduce a practical bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Preliminary experiments suggest that this approach offers a practical and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.

Problem

• Develop scalable conditional independence tests using spectral representations
• Address limitations of kernel methods in adaptivity and convergence
• Bridge kernel-based theory with representation learning for validity

Innovation

• Spectral representations from partial covariance operator decomposition
• Bi-level contrastive algorithm for learning these representations
• Test statistic similar to HSIC for scalable CI testing