Nonlinear Independent Component Analysis for Continuous-Time Signals

We study the classical problem of recovering a multidimensional source process from observations of nonlinear mixtures of this process. Assuming statistical independence of the coordinate processes of the source, we show that this recovery is possible for many popular models of stochastic processes (up to order and monotone scaling of their coordinates) if the mixture is given by a sufficiently differentiable, invertible function. Key to our approach is the combination of tools from stochastic analysis and recent contrastive learning approaches to nonlinear ICA. This yields a scalable method with widely applicable theoretical guarantees for which our experiments indicate good performance.