This paper presents a new approach to the blind source separation problem. This approach is based on a formulation of blind separation as a problem of learning and inference in a dynamic graphical model. In this model, the sources are described by independent hidden Markov models, which capture not only the one-point histogram but also temporal structure of the sources. Using the model, we derive unsupervised learning algorithms that learn the source densities and temporal structure, as well as the mixing matrix, from the observed data. Inference in this model provides an optimal reconstruction of the sources from data. We present demonstrate an expectation-maximization algorithm for square, zero-noise mixing, and algorithms for the general case,where the number of sources may differ from the number of observed mixtures and the data are noisy. In the latter case, the complexity of the graphical model makes exact learning and inference computationally intractable. An approximate algorithm based on the variational approach, which maximizes a lower bound on the likelihood, is presented and shown to be quite accurate.
展开▼
