Deep Independent Component Analysis for Time Series with Invertible Neural Networks

Independent Component Analysis (ICA) is a critical tool for identifying latent independent signals within multivariate observations, and has wide applications in fields such as financial time series and biomedical engineering. However, conventional ICA methods are primarily limited to linear transformations and assume independent observations, often failing to capture the complex dependence structures and time-dependent data. To address this, we develop a nonlinear ICA method for time series data. Our approach leverages an energy-distance-based loss function for indepdence measurement, and employs invertible neural networks (INN) to model nonlinear invertible mappings. We further derive theoretical properties of the INN function class, including its approximation capacity and pseodu-dimension, which are essential to establish the convergence rate of the nonlinear ICA estimator.