Reviews: Likelihood-Free Overcomplete ICA and Applications In Causal Discovery

Overcomplete ICA (more sources than data) often becomes feasible after making a parametric assumption on the distribution of sources to make the computation of the likelihood feasible. The authors have proposed a method to estimate the mixing matrix without computing the likelihood. The proposed method is minimizing a distributional distance (MMD) between the generated and observed data when each source is produced by a nonlinear transformation of an independent noise. The generation procedure makes sure that sources are independent. The mixing matrix and the parameters of the generator of each source distribution are learned together.