Linear Independent Component Analysis (ICA) recovers jointly independent source signals from their linear mixtures. To achieve this, classical ICA algorithms attempt to maximize non-Gaussianity, measured by negentropy, which is linked to independence by information theory. Because exact negentropy optimization is intractable, they rely on proxy contrast functions, such as fourth-order cumulants, and parametric log-likelihoods. We propose instead to measure non-Gaussianity using the squared Wasserstein distance $W_2^2$ to a standard Gaussian. We prove that the Wasserstein distance between a standard normal distribution and linear projections of the data is maximized when the projection recovers an independent component. Based on this observation, we propose the OT-ICA algorithm which finds this projection by gradient-based optimization. Empirical evaluation on simulated data shows that OT-ICA outperforms proxy-based methods for different distributions of the latent variables. Application to EEG artifact removal and econometric price discovery confirm OT-ICA can be used for applied ICA tasks without distributional assumptions.
Ashutosh Jha, M. Besserve, Simon Buchholz· 1 citation
We study a general class of gradient interface models with Hamiltonian $H=\beta\sum V(\nabla\phi)$, $\beta>0$, assuming essentially that the potential $V$ is even, $V'(s)\ge \alpha s$ on $[0,\infty)$ for some $\alpha>0$, and $-M\leq V''\le C$. We establish a Helffer-Sj\"ostrand representation for these models, and use it to prove that their scaling limits are Gaussian Free Fields (GFFs), and that their covariances decay at the same rate as the GFF. This extends results for strictly convex potentials to a large class of non-convex potentials and to arbitrary temperatures. Additionally, we prove Brascamp-Lieb and dimension-free Poincar\'e inequalities for the models. We obtain these results by representing the interface as a mixture of gradient interface models with strictly convex potentials, extending an idea by Biskup-Spohn who had considered mixtures of Gaussians at moderate inverse temperature $\beta=1$. The construction of such a representation is one of the key new contributions of this work.
Simon Buchholz, Codina Cotar, Florian Schweiger· 0 citations