A Dictionary Learning Approach for Factorial Gaussian Models
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In this paper, we develop a parameter estimation method for factorially parametrized models such as Factorial Gaussian Mixture Model and Factorial Hidden Markov Model. Our contributions are two-fold. First, we show that the emission matrix of the standard Factorial Model is unidentifiable even if the true assignment matrix is known. Secondly, we address the issue of identifiability by making a one component sharing assumption and derive a parameter learning algorithm for this case. Our approach is based on a dictionary learning problem of the form X = O R, where the goal is to learn the dictionary O given the data matrix X. We argue that due to the specific structure of the activation matrix R in the shared component factorial mixture model, and an incoherence assumption on the shared component, it is possible to extract the columns of the O matrix without the need for alternating between the estimation of O and R.
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