Hidden semi-Markov models

Abstract

As an extension to the popular hidden Markov model (HMM), a hidden semi-Markov model (HSMM) allows the underlying stochastic process to be a semi-Markov chain. Each state has variable duration and a number of observations being produced while in the state. This makes it suitable for use in a wider range of applications. Its forwardbackward algorithms can be used to estimate/update the model parameters, determine the predicted, filtered and smoothed probabilities, evaluate goodness of an observation sequence fitting to the model, and find the best state sequence of the underlying stochastic process. Since the HSMM was initially introduced in 1980 for machine recognition of speech, it has been applied in thirty scientific and engineering areas, such as speech recognition/synthesis, human activity recognition/prediction, handwriting recognition, functional MRI brain mapping, and network anomaly detection. There are about three hundred papers published in the literature. An overview of HSMMs is presented in this paper, including modelling, inference, estimation, implementation and applications. It first provides a unified description of various HSMMs and discusses the general issues behind them. The boundary conditions of HSMM are extended. Then the conventional models, including the explicit duration, variable transition, and residential time of HSMM, are discussed. Various duration distributions and observation models are presented. Finally, the paper draws an outline of the applications.

Modeling Content Structures of Domain-Specific Texts with RUP-HDP-HSMM and Its Applications

“…To overcome these weaknesses, the hierarchical Dirichlet process hidden semi-Markov model (HDP-HSMM) is proposed [4], which can explicitly specify the distributions of duration times of hidden states as traditional hidden semi-Markov models (HSMM) [9], and can infer the number of hidden states in the nonparametric settings as HDP-HMM [5]. However, as discussed earlier, simple duration distributions, usually employed in conventional HDP-HSMMs, cannot properly model the complicated duration times of local contexts in real-world texts.…”

Performance analysis of orthogonal frequency division multiplexing systems in dispersive indoor power line channels inflicting asynchronous impulsive noise

“…The HSMM [27] is an extension of the classic hidden Markov model [31], where the underlying stochastic process obeys a semi-Markov chain, while the different states may have different durations [28]. Based on the HSMM, below we show a noise model for PLC.…”

“…where p(k) is given in (28). In (30), P e (g i,k ) is the BER of Q-ary QAM employing Gray coding for a given SNR g i,k , which can be expressed in a generalised form as [33,34] …”

“…Against this background, our new contribution is that the hidden semi-Markov model (HSMM) [27], which was shown to accurately model the duration of burst events in [28], is applied for modelling the bursty behaviour of asynchronous IN, when analytically characterising the bit error ratio (BER) performance of orthogonal frequency division multiplexing (OFDM)-based PLC systems using Q-ary quadrature amplitude modulation (QAM). Our simulation results verify the accuracy of our analytical results.…”

Phrase-Based Statistical Model for Korean Morpheme Segmentation and POS Tagging

“…To find the segmentation result that maximizes score(x, y), we use an extension of the decoding algorithm for the hidden semi-Markov model (HSMM) [27], by taking a phrase lattice as an input. In a phrase lattice, the state of each node is uniquely specified by (i,t), wheret represents the last N − 1 POS tags ending at the i-th syllable given this state.…”