Signal Decomposition using Multiscale Admixture Models

Admixture models are "mixtures of mixtures" that decompose an object into multiple latent components, with the component proportions varying stochastically across objects. Recent work in machine learning has successfully developed admixture models for text, and work in population genetics has developed such models to analyze complex groups of individuals having mixed ancestry. We introduce a family of graphical admixture models for decomposing a signal into multiple components based on a wavelet representation of the signal. Two models are developed, one using a fixed segmentation of the signal, another using recursive dyadic partitioning. Variational algorithms are derived for inferring mixture proportions and estimating parameters.