Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.04276 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917059131080704 |
|---|---|
| author | Ramsey, Joseph Andrews, Bryan Spirtes, Peter |
| author_facet | Ramsey, Joseph Andrews, Bryan Spirtes, Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalable Causal Discovery from Recursive Nonlinear Data via Truncated Basis Function Scores and Tests Ramsey, Joseph Andrews, Bryan Spirtes, Peter Machine Learning Artificial Intelligence 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. |
| title | Scalable Causal Discovery from Recursive Nonlinear Data via Truncated Basis Function Scores and Tests |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2510.04276 |