Time-inhomogeneous hidden Bernoulli model

Time-Inhomogeneous Hidden Bernoulli Model (TI-HBM) is an alternative to Hidden Markov Model (HMM) 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 (an independent) 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 $O(NL)$ (instead of $O(N^{2}L)$ in the HMM case, where $N$ and $L$ are number of states and observation sequence length respectively). The TI-HBM is able to model acoustic-unit duration (e.g. phone/word 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.
For details, see [1] or [2].

[1] Jahanshah Kabudian, M. Mehdi Homayounpour, S. Mohammad Ahadi, "Bernoulli versus Markov: Investigation of state transition regime in switching-state acoustic models," Signal Processing, vol. 89, no. 4, pp. 662-668, April 2009.
[2] Jahanshah Kabudian, M. Mehdi Homayounpour, S. Mohammad Ahadi, "Time-inhomogeneous hidden Bernoulli model: An alternative to hidden Markov model for automatic speech recognition," Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4101-4104, Las Vegas, Nevada, USA, March 2008.