Post-Nonlinear Causal Relationship with Finite Samples: A Maximal Correlation Perspective
Primary Area: causal reasoning
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: Causal Discovery, Post-Nonlinear, Maximal Correlation
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
Abstract: Bivariate causal discovery aims to determine the causal relationship between two random variables from passive observational data (as intervention is not affordable in many scientific fields), which is considered fundamental and challenging. Designing algorithms based on the post-nonlinear (PNL) model has aroused much attention for its generality. However, the state-of-the-art (SOTA) PNL-based algorithms involve highly non-convex objectives due to the use of neural networks and non-convex losses, thus optimizing such objectives is often time-consuming and unable to produce meaningful solutions with finite samples. In this paper, we propose a novel method that incorporates maximal correlation into the PNL model learning (short as MC-PNL) such that the underlying nonlinearities can be accurately recovered. Owing to the benign structure of our objective function, when modeling the nonlinearities with linear combinations of random Fourier features, the target optimization problem can be solved rather efficiently and rapidly via the block coordinate descent. We also compare the MC-PNL with SOTA methods on the downstream synthetic and real causal discovery tasks to show its superiority in time and accuracy. Our code is available at https://anonymous.4open.science/r/MC-PNL-3C09/.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 5258
Loading