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I just read about Linear dynamical systems and I already know HMM. I wonder if HMMs are a special case of LDS or are there good relations. (Both were compared by Geoffrey Hinton in one of his lectures to Recurrent Neural Networks.) Or are there other types of continuous HMM (where the internal state space is continuous)? |
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Yes. Given probabilities on the current state it's a linear operation to get probabilities on the next state, or the next emissions, if your output probabilities are linear. |
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Just to add a bit to Alexandre great answer. This can be extended to pretty much any Linear Gaussian System as well, that is, the case when the transition probabilities and the observation probabilities are both Gaussian (also called Kalman Filters) In the paper they unify all these models on the same basic premises. As an historical anecdote, both HMM and Kalman Filters were discovered by different people in the 60s, but only until the 90s they were really unified. |
