Algebraic identifiability in independent component analysis mixture models

In this talk, we discuss independent component analysis (ICA) mixture models. These models consist of mixtures of ICA densities. An ICA density is associated with a random vector whose coordinates become mutually independent after an invertible linear transformation. In particular, ICA mixture models are nonparametric extensions of the celebrated family of Gaussian mixtures. We establish when the mixing coefficients, linear transformations, and source moments are recoverable, up to a finite class, from observed moments of order at most $d$. For n-variate distributions and $d >= 3$, we prove algebraic identifiability for models with asymptotically up to $1/d!$ $n^(d-2)$ mixture components, and discuss a method-of-moments algorithm for density estimation over these models.