Scalable Causal Discovery from Recursive Nonlinear Data via Truncated Basis Function Scores and Tests

• URL: http://arxiv.org/abs/2510.04276v2
• Date: Tue, 04 Nov 2025 17:31:04 GMT
• Title: Scalable Causal Discovery from Recursive Nonlinear Data via Truncated Basis Function Scores and Tests
• Authors: Joseph Ramsey, Bryan Andrews, Peter Spirtes,
• Abstract summary: We introduce two basis-expansion tools for scalable causal discovery.<n>First, the Basis Function BIC score uses truncated additive expansions to approximate nonlinear dependencies.<n>Second, the Basis Function Likelihood Ratio Test (BF-LRT) provides an approximate conditional independence test.
• Score: 7.021824046220355
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning graphical conditional independence structures from nonlinear, continuous or mixed data is a central challenge in machine learning and the sciences, and many existing methods struggle to scale to thousands of samples or hundreds of variables. We introduce two basis-expansion tools for scalable causal discovery. First, the Basis Function BIC (BF-BIC) score uses truncated additive expansions to approximate nonlinear dependencies. BF-BIC is theoretically consistent under additive models and extends to post-nonlinear (PNL) models via an invertible reparameterization. It remains robust under moderate interactions and supports mixed data through a degenerate-Gaussian embedding for discrete variables. In simulations with fully nonlinear neural causal models (NCMs), BF-BIC outperforms kernel- and constraint-based methods (e.g., KCI, RFCI) in both accuracy and runtime. Second, the Basis Function Likelihood Ratio Test (BF-LRT) provides an approximate conditional independence test that is substantially faster than kernel tests while retaining competitive accuracy. Extensive simulations and a real-data application to Canadian wildfire risk show that, when integrated into hybrid searches, BF-based methods enable interpretable and scalable causal discovery. Implementations are available in Python, R, and Java.

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