  Independent component analysis (ICA) is a blind source separation method for
linear disentanglement of independent latent sources from observed data. We
investigate the special setting of noisy linear ICA where the observations are
split among different views, each receiving a mixture of shared and individual
sources. We prove that the corresponding linear structure is identifiable, and
the source distribution can be recovered. To computationally estimate the
sources, we optimize a constrained form of the joint log-likelihood of the
observed data among all views. We also show empirically that our objective
recovers the sources also in the case when the measurements are corrupted by
noise. Furthermore, we propose a model selection procedure for recovering the
number of shared sources which we verify empirically. Finally, we apply the
proposed model in a challenging real-life application, where the estimated
shared sources from two large transcriptome datasets (observed data) provided
by two different labs (two different views) lead to recovering (shared) sources
utilized for finding a plausible representation of the underlying graph
structure.
