Nonlinear ICA

Nonlinear independent component analysis (ICA) aims to recover underlying independent sources from their nonlinearly mixed observations, a challenging problem with implications for various fields. Recent research focuses on developing robust algorithms, often employing variational autoencoders or Gaussian process-based models, to address identifiability issues—ensuring the unique recovery of the original sources—particularly in scenarios with high-dimensional or spatially structured data. This work is driven by the need for more flexible and generalizable methods that relax assumptions like strict sparsity or complete independence among sources, thereby expanding the applicability of nonlinear ICA to complex real-world datasets. Improved nonlinear ICA techniques promise advancements in areas such as disentangled representation learning, causal inference, and the analysis of complex dynamical systems.