Using Mixture of Gaussians to Compare Approaches to Signal Separation

Signal separation techniques come in countless different types and variants. Often many of these belong to certain subset of techniques such as Independent Component Analysis (ICA), but even within such a subset it can be hard or impossible to compare the different approaches. In this paper is an example of how such different approaches to separation can be compared using Mixtures of Gaussians as a prior distribution. This not only illuminates some interesting properties of Maximum Likelihood and Energy Based Models, but is also an example of how Mixtures of Gaussians can serve as a both flexible and analytically tractable family of distributions.