Large Deviation Bounds for Functionals of Viterbi Paths

Ghosh, Arka P.; Kleiman, Elena; Roitershtein, Alexander

doi:10.1109/tit.2011.2132550

Cited by 7 publications

(9 citation statements)

References 18 publications

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“…Assuming that the asymptotic risk R 1 has been found (by simulations, for example), one could now be interested in a large deviation type upper bound on P( Ghosh et al, 2009) it has been shown that under the same assumptions as in the present paper, the following large deviation principle holds:…”

Section: The R 1 -Riskmentioning

confidence: 78%

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Theory of Segmentation

Lember¹,

Kuljus²,

Koloydenko³

2011

Hidden Markov Models, Theory and Applications

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Section: The R 1 -Riskmentioning

confidence: 78%

“…The authors of (Ghosh et al, 2009) do not state the exact bound on the probability P(R 1 (v, Y n , X n ) − R 1 > ǫ), but it could be derived from their proof of the above result. We would like to draw the reader's attention to how this theme is different from supervised learning.…”

Section: The R 1 -Riskmentioning

confidence: 99%

Theory of Segmentation

Lember¹,

Kuljus²,

Koloydenko³

2011

Hidden Markov Models, Theory and Applications

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“…The results of the present paper are largely based on the following theorem, which has been proved in [18,17]. See also Lemma 2.1 in [8].…”

Section: One-sided Infinite Viterbi Alignmentmentioning

confidence: 90%

Asymptotic risks of Viterbi segmentation

Kuljus

Lember

2012

Stochastic Processes and their Applications

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We consider the maximum likelihood (Viterbi) alignment of a hidden Markov model (HMM). In an HMM, the underlying Markov chain is usually hidden and the Viterbi alignment is often used as the estimate of it. This approach will be referred to as the Viterbi segmentation. The goodness of the Viterbi segmentation can be measured by several risks. In this paper, we prove the existence of asymptotic risks. Being independent of data, the asymptotic risks can be considered as the characteristics of the model that illustrate the long-run behavior of the Viterbi segmentation.

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“…When it is ensured that (Z, V ) is regenerative, the standard theory for regenerative processes can be applied. See [1,10,14,15] for regeneration-based inferences of HMM. It is important to stress that the regenerativity of (Z, V ) is possible due to the existence of barriers and that is an extra motivation of barrier construction studied in this paper.…”

Section: Viterbi Pathmentioning

confidence: 99%

“…Then b 1:M is a 1-barrier of order M − l. If inequalities (15) are strict for any i, j and any k = 1 for which the left side of the inequality is non-zero, then b 1:M is a strong 1-barrier of order M − l.…”

Section: Barrier Set Construction Theoremmentioning

confidence: 99%

Existence of infinite Viterbi path for pairwise Markov models

Lember

Sova

2020

Stochastic Processes and their Applications

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For hidden Markov models one of the most popular estimates of the hidden chain is the Viterbi path -the path maximising the posterior probability. We consider a more general setting, called the pairwise Markov model, where the joint process consisting of finite-state hidden regime and observation process is assumed to be a Markov chain. We prove that under some conditions it is possible to extend the Viterbi path to infinity for almost every observation sequence which in turn enables to define an infinite Viterbi decoding of the observation process, called the Viterbi process. This is done by constructing a block of observations, called a barrier, which ensures that the Viterbi path goes trough a given state whenever this block occurs in the observation sequence.

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Large Deviation Bounds for Functionals of Viterbi Paths

Cited by 7 publications

References 18 publications

Theory of Segmentation

Theory of Segmentation

Asymptotic risks of Viterbi segmentation

Existence of infinite Viterbi path for pairwise Markov models

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