Book Chapter10.1007/978-3-319-11433-0_11
Robustifying the Viterbi Algorithm
Cedric De Boom,Jasper De Bock,Arthur Van Camp,Gert de Cooman +3 more
- 17 Sep 2014
- Vol. 8754, pp 160-175
TL;DR: An efficient algorithm for estimating hidden state sequences in imprecise hidden Markov models (iHMMs), based on observed output sequences, that considers as estimates for the hidden state sequence those sequences that are maximal.
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Abstract: We present an efficient algorithm for estimating hidden state sequences in imprecise hidden Markov models (iHMMs), based on observed output sequences. The main difference with classical HMMs is that the local models of an iHMM are not represented by a single mass function, but rather by a set of mass functions. We consider as estimates for the hidden state sequence those sequences that are maximal. In this way, we generalise the problem of finding a state sequence with highest posterior probability, as is commonly considered in HMMs, and solved efficiently by the Viterbi algorithm. An important feature of our approach is that there may be multiple maximal state sequences, typically for iHMMs that are highly imprecise. We show experimentally that the time complexity of our algorithm tends to be linear in this number of maximal sequences, and investigate how this number depends on the local models.
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References
A tutorial on hidden Markov models and selected applications in speech recognition
Lawrence R. Rabiner
- 01 Feb 1989
TL;DR: In this paper, the authors provide an overview of the basic theory of hidden Markov models (HMMs) as originated by L.E. Baum and T. Petrie (1966) and give practical details on methods of implementation of the theory along with a description of selected applications of HMMs to distinct problems in speech recognition.
Error bounds for convolutional codes and an asymptotically optimum decoding algorithm
TL;DR: The upper bound is obtained for a specific probabilistic nonsequential decoding algorithm which is shown to be asymptotically optimum for rates above R_{0} and whose performance bears certain similarities to that of sequential decoding algorithms.
7.6K
Inferences from Multinomial Data: Learning About a Bag of Marbles
TL;DR: In this article, the imprecise Dirichlet model is proposed for multinomial data in cases where there is no prior information and the probabilities are expressed in terms of posterior upper and lower probabilities.
557
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