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An excellent, approachable review that unifies these approaches is A Unifying Review of Linear Gaussian Models by Roweis and Ghahramani, published in Neural Computation. The first two sentences of the abstract are Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models ...


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This is a nice example that shows a number of potential issues when using state space models, so there are a number of suggestions that I can make that might be helpful. First, I'll describe what I think is the solution here, and then I'll describe a few more things that may be helpful. Parameter estimation instability The main issue you brought up was ...


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