Statistical Inference in Hidden Markov Models Using k-Segment Constraints
Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence o...
| Main Authors: | , , |
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| Format: | Journal article |
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Taylor and Francis
2016
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| _version_ | 1826262175828672512 |
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| author | Titsias, M Holmes, C Yau, C |
| author_facet | Titsias, M Holmes, C Yau, C |
| author_sort | Titsias, M |
| collection | OXFORD |
| description | Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward–backward algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions k-segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of k-segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online. |
| first_indexed | 2024-03-06T19:32:15Z |
| format | Journal article |
| id | oxford-uuid:1dd90c62-4cb5-45b8-b338-8827fc40114a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:32:15Z |
| publishDate | 2016 |
| publisher | Taylor and Francis |
| record_format | dspace |
| spelling | oxford-uuid:1dd90c62-4cb5-45b8-b338-8827fc40114a2022-03-26T11:13:13ZStatistical Inference in Hidden Markov Models Using k-Segment ConstraintsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1dd90c62-4cb5-45b8-b338-8827fc40114aSymplectic Elements at OxfordTaylor and Francis2016Titsias, MHolmes, CYau, CHidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward–backward algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions k-segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of k-segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online. |
| spellingShingle | Titsias, M Holmes, C Yau, C Statistical Inference in Hidden Markov Models Using k-Segment Constraints |
| title | Statistical Inference in Hidden Markov Models Using k-Segment Constraints |
| title_full | Statistical Inference in Hidden Markov Models Using k-Segment Constraints |
| title_fullStr | Statistical Inference in Hidden Markov Models Using k-Segment Constraints |
| title_full_unstemmed | Statistical Inference in Hidden Markov Models Using k-Segment Constraints |
| title_short | Statistical Inference in Hidden Markov Models Using k-Segment Constraints |
| title_sort | statistical inference in hidden markov models using k segment constraints |
| work_keys_str_mv | AT titsiasm statisticalinferenceinhiddenmarkovmodelsusingksegmentconstraints AT holmesc statisticalinferenceinhiddenmarkovmodelsusingksegmentconstraints AT yauc statisticalinferenceinhiddenmarkovmodelsusingksegmentconstraints |