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Time-inhomogeneous hidden Bernoulli model is an alternative to hidden Markov model for automatic speech recognition. Contrary to HMM, the state transition process in TI-HBM is not a Markov-dependent process, rather it is a generalized Bernoulli process. This difference leads to elimination of dynamic programming at state-level in TI-HBM decoding process. Thus, the computational complexity of TI-HBM for probability evaluation and state estimation is O {\displaystyle O} {\displaystyle O} in the HMM case, where N {\displaystyle N} and L {\displaystyle L} are number of states and observation sequence length respectively]. The TI-HBM is able to model acoustic-unit duration by using a built-in parameter named survival probability. The TI-HBM is simpler and faster than HMM in a phoneme recognition task, but its performance is comparable to HMM.
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