Multi-View Independent Component Analysis with Shared and Individual Sources

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 shared sources can be recovered, provided that sufficiently many diverse views and data points are available. To computationally estimate the sources, we optimize a constrained form of the joint log-likelihood of the observed data among all views. We show empirically that our objective recovers the sources in high dimensional settings, also in the case when the measurements are corrupted by noise. 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 a more plausible representation of the underlying graph structure than existing baselines.