Fourier Feature Methods for Nonlinear Causal Discovery

An arXiv preprint (2605.05743) introduces two new approaches using Fourier features for discovering nonlinear causal relationships. The first method, the Fourier Feature Marginal Likelihood (FFML) score, simplifies the marginal likelihood estimation of Gaussian processes by replacing the large kernel Gram matrix with a more manageable finite-dimensional feature representation. This adjustment reduces the complexity to O(nm^2 + m^3). It can handle various combinations of continuous and discrete variables through a product-kernel method. The second innovation, the Fourier Feature Conditional Independence (FFCI) test, provides a quick, nonparametric way to test for conditional independence in mixed datasets. Together, these methods enhance the toolkit for different causal discovery strategies while overcoming the limitations of traditional Gaussian process techniques.