Score-based Generative Modeling for Conditional Independence Testing
Journal:
arXiv
Published Date:
May 29, 2025
Abstract
Determining conditional independence (CI) relationships between random
variables is a fundamental yet challenging task in machine learning and
statistics, especially in high-dimensional settings. Existing generative
model-based CI testing methods, such as those utilizing generative adversarial
networks (GANs), often struggle with undesirable modeling of conditional
distributions and training instability, resulting in subpar performance. To
address these issues, we propose a novel CI testing method via score-based
generative modeling, which achieves precise Type I error control and strong
testing power. Concretely, we first employ a sliced conditional score matching
scheme to accurately estimate conditional score and use Langevin dynamics
conditional sampling to generate null hypothesis samples, ensuring precise Type
I error control. Then, we incorporate a goodness-of-fit stage into the method
to verify generated samples and enhance interpretability in practice. We
theoretically establish the error bound of conditional distributions modeled by
score-based generative models and prove the validity of our CI tests. Extensive
experiments on both synthetic and real-world datasets show that our method
significantly outperforms existing state-of-the-art methods, providing a
promising way to revitalize generative model-based CI testing.
