Nonlinear Independent Component Analysis for Discrete-Time and Continuous-Time Signals

Understand

We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal.

• We show that this recovery is possible (up to a permutation and monotone scaling of the source's original component signals) if the mixture is due to a sufficiently differentiable and invertible but otherwise arbitrarily nonlinear function and the component signals of the source are statistically independent with 'non-degenerate' second-order statistics.
• The latter assumption requires the source signal to meet one of three regularity conditions which essentially ensure that the source is sufficiently far away from the non-recoverable extremes of being deterministic or constant in time.
• These assumptions, which cover many popular time series models and stochastic processes, allow us to reformulate the initial problem of nonlinear blind source separation as a simple-to-state problem of optimisation-based function approximation.