Identifiability of overcomplete independent component analysis

ndependent component analysis (ICA) is a classical data analysis method to study mixtures of independent sources. An ICA model is said to be identifiable if the mixing can be recovered uniquely. Identifiability is known to hold if and only if at most one of the sources is Gaussian, provided the number of sources is at most the number of observations. In this talk, I will discuss our work to generalize the identifiability of ICA to the overcomplete setting, where the number of sources can exceed the number of observations. The underlying problem is algebraic and the proof studies linear spaces of rank one symmetric matrices. Based on joint work with Anna Seigal arxiv.org/abs/2401.14709.