Wasserstein Distance Powers New Contrast-Free ICA and Causal Inference Method

In a new preprint, Laplante, Ambroise, and Humbert propose using the squared 2-Wasserstein distance to the standard Gaussian as a non-Gaussianity measure for linear Independent Component Analysis (ICA) and causal inference in Linear Non-Gaussian Acyclic Models (LiNGAM). Traditional ICA relies on contrast functions like kurtosis or negentropy, but these can struggle with finite samples or require careful optimization. The authors show that for independent standardized sources with at most one Gaussian, any unit-norm linear combination involving at least two sources has a strictly smaller squared Wasserstein distance than the weighted sum of source distances. This yields exact identification of the ICA unmixing matrix up to signed permutation and gives an analogous characterization of causal orders through least-squares residuals.

On the practical side, the team develops empirical plug-in estimators with distribution-free uniform convergence bounds under finite-moment assumptions. They then implement three distinct solvers: a Picard-style orthogonal optimizer for ICA, an exhaustive dynamic programming algorithm for causal-order search, and a greedy variant for larger datasets. Experiments demonstrate competitive performance against state-of-the-art methods on both source separation and causal inference benchmarks. Open-source code is provided, making this contrast-free approach immediately usable for real-world applications where non-Gaussianity is a key assumption.