Hidden semi-Markov model
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A hidden semi-Markov model (HSMM) is a hidden Markov model in which the number of outputs generated before moving to a new - but not necessarily different - hidden state is a random variable, with a certain probability to occur. It is therefore able to generate more than one output per state transition, or to map the current state in probabilistics terms.
Let x denote the hidden state sequence. The hidden state variable takes on T values (i.e. pass through T states) while generating the output sequence y whose length is I. Unlike the standard hidden Markov model the number of transitions in the hidden sequence need not be equal to the length of the output, since while in state xt more than one output symbol may be generated. Nevertheless, the sum of the lengths of the outputs of the T different state transitions must be I.
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