An extension of the ICA model using latent variables

The Independent Component Analysis (ICA) model is extended to the case where the components are not necessarily independent: depending on the value a hidden latent process at the same time, the unknown components of the linear mixture are assumed either mutually independent or dependent. We propose for this model a separation method which combines: (i) a classical ICA separation performed using the set of samples whose components are conditionally independent, and (ii) a method for estimation of the latent process. The latter task is performed by Iterative Conditional Estimation (ICE). It is an estimation technique in the case of incomplete data, which is particularly appealing because it requires only weak conditions. Finally, simulations validate our method and show that the separation quality is improved for sources generated according to our model.