Hidden Markov model: Difference between revisions

Revision as of 00:18, 18 September 2023

Revision as of 14:18, 20 November 2023

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=== Statistical significance ===

For some of the above problems, it may also be interesting to ask about [[statistical significance]]. What is the probability that a sequence drawn from some [[null distribution]] will have an HMM probability (in the case of the forward algorithm) or a maximum state sequence probability (in the case of the Viterbi algorithm) at least as large as that of a particular output sequence?<ref>{{Cite journal |last1=Newberg |first1=L. |doi=10.1186/1471-2105-10-212 |title=Error statistics of hidden Markov model and hidden Boltzmann model results |journal=BMC Bioinformatics |volume=10 |pages=212 |year=2009 |pmid=19589158 |pmc=2722652 |doi-access=free }} {{open access}}</ref> When an HMM is used to evaluate the relevance of a hypothesis for a particular output sequence, the statistical significance indicates the [[false positive rate]] associated with failing to reject the hypothesis for the output sequence.

== Learning ==

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* [[Computational finance]]<ref>{{cite journal |doi=10.1007/s10614-016-9579-y |volume=49 |issue=4 |title=Parallel Optimization of Sparse Portfolios with AR-HMMs |year=2016 |journal=Computational Economics |pages=563–578 |last1=Sipos |first1=I. Róbert |last2=Ceffer |first2=Attila |last3=Levendovszky |first3=János|s2cid=61882456 }}</ref><ref>{{cite journal |doi=10.1016/j.eswa.2016.01.015 |volume=53 |title=A novel corporate credit rating system based on Student's-t hidden Markov models |year=2016 |journal=Expert Systems with Applications |pages=87–105 |last1=Petropoulos |first1=Anastasios |last2=Chatzis |first2=Sotirios P. |last3=Xanthopoulos |first3=Stylianos}}</ref>

* [[Single-molecule experiment|Single-molecule kinetic analysis]]<ref>{{cite journal |doi=10.1142/S1793048013300053 |title=SOLVING ION CHANNEL KINETICS WITH THE QuB SOFTWARE |journal=Biophysical Reviews and Letters |date=2013 |volume=8 |issue=3n04 |pages=191–211 |first=CHRISTOPHER |last=NICOLAI}}</ref>

* [[Neuroscience]]<ref>{{cite journal |doi=10.1002/hbm.25835 |title=Spatiotemporally Resolved Multivariate Pattern Analysis for M/EEG |journal=Human Brain Mapping |date=2022 |last1=Higgins |first1=Cameron |last2=Vidaurre |first2=Diego |last3=Kolling |first3=Nils |last4=Liu |first4=Yunzhe |last5=Behrens | first5=Tim | last6=Woolrich | first6=Mark|volume=43 |issue=10 |pages=3062–3085 |pmid=35302683 |pmc=9188977 }}</ref><ref>{{Cite journal |lastlast1=Diomedi |firstfirst1=S. |last2=Vaccari |first2=F. E. |last3=Galletti |first3=C. |last4=Hadjidimitrakis |first4=K. |last5=Fattori |first5=P. |date=2021-10-01 |title=Motor-like neural dynamics in two parietal areas during arm reaching |url=https://www.sciencedirect.com/science/article/pii/S0301008221001301 |journal=Progress in Neurobiology |language=en |volume=205 |pages=102116 |doi=10.1016/j.pneurobio.2021.102116 |pmid=34217822 |issn=0301-0082|hdl=11585/834094 |s2cid=235703641 |hdl-access=free }}</ref>

* [[Cryptanalysis]]

* [[Speech recognition]], including [[Siri]]<ref>{{cite book|last1=Domingos|first1=Pedro|title=The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World|url=https://archive.org/details/masteralgorithmh0000domi|url-access=registration|date=2015|publisher=Basic Books|isbn=9780465061921|page=[https://archive.org/details/masteralgorithmh0000domi/page/37 37]|language=en}}</ref>

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== History ==

Hidden Markov models were described in a series of statistical papers by [[Leonard E. Baum]] and other authors in the second half of the 1960s.<ref>{{cite journal |last=Baum |first=L. E. |author2=Petrie, T. |title=Statistical Inference for Probabilistic Functions of Finite State Markov Chains |journal=The Annals of Mathematical Statistics |year=1966 |volume=37 |issue=6 |pages=1554–1563 |doi=10.1214/aoms/1177699147|doi-access=free }}</ref><ref>{{Cite journal |last1=Baum |first1=L. E. |last2=Eagon |first2=J. A. |doi=10.1090/S0002-9904-1967-11751-8 |title=An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology |journal=[[Bulletin of the American Mathematical Society]] |volume=73 |issue=3 |pages=360 |year=1967 |zbl=0157.11101 |url=http://projecteuclid.org/euclid.bams/1183528841 |doi-access=free }}</ref><ref>{{cite journal |last=Baum |first=L. E. |author2=Sell, G. R. |title=Growth transformations for functions on manifolds |journal=Pacific Journal of Mathematics |year=1968 |volume=27 |issue=2 |pages=211–227 |url=https://www.scribd.com/doc/6369908/Growth-Functions-for-Transformations-on-Manifolds |access-date=28 November 2011 |doi=10.2140/pjm.1968.27.211 |doi-access=free |archive-date=18 March 2014 |archive-url=https://web.archive.org/web/20140318223209/http://www.scribd.com/doc/6369908/Growth-Functions-for-Transformations-on-Manifolds |url-status=dead }}</ref><ref>{{Cite journal |last1=Baum |first1=L. E. |author-link1=Leonard E. Baum |last2=Petrie |first2=T. |last3=Soules |first3=G. |last4=Weiss |first4=N. |title=A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains |doi=10.1214/aoms/1177697196 |journal=[[The Annals of Mathematical Statistics]] |volume=41 |issue=1 |pages=164–171 |year=1970 |jstor=2239727 |zbl=0188.49603 |mr=287613 |doi-access=free }}</ref><ref>{{cite journal |last=Baum |first=L.E. |title=An Inequality and Associated Maximization Technique in Statistical Estimation of Probabilistic Functions of a Markov Process |journal=Inequalities |year=1972 |volume=3 |pages=1–8}}</ref> One of the first applications of HMMs was [[speech recognition]], starting in the mid-1970s.<ref>{{Cite journal |last1=Baker |first1=J. |author-link1=James K. Baker |doi=10.1109/TASSP.1975.1162650 |title=The DRAGON system—An overview |journal=IEEE Transactions on Acoustics, Speech, and Signal Processing |volume=23 |pages=24–29 |year=1975 }}</ref><ref>{{Cite journal |last1=Jelinek |first1=F. |last2=Bahl |first2=L. |last3=Mercer |first3=R. |doi=10.1109/TIT.1975.1055384 |title=Design of a linguistic statistical decoder for the recognition of continuous speech |journal=[[IEEE Transactions on Information Theory]] |volume=21 |issue=3 |pages=250 |year=1975 }}</ref><ref>{{cite book |title=Hidden Markov Models for Speech Recognition |publisher=Edinburgh University Press |year=1990 |isbn=978-0-7486-0162-2 |author1=Xuedong Huang |author2=M. Jack |author3=Y. Ariki |author-link1=Xuedong Huang}}</ref><ref>{{cite book |title=Spoken Language Processing |publisher=Prentice Hall |year=2001 |isbn=978-0-13-022616-7 |author1=Xuedong Huang |author2=Alex Acero |author3=Hsiao-Wuen Hon |author-link1=Xuedong Huang}}</ref>

In the second half of the 1980s, HMMs began to be applied to the analysis of biological sequences,<ref>{{cite journal |doi=10.1016/0022-2836(86)90289-5 |author=M. Bishop and E. Thompson |title=Maximum Likelihood Alignment of DNA Sequences |journal=[[Journal of Molecular Biology]] |volume=190 |issue=2 |pages=159–165 |year=1986 |pmid=3641921}} {{subscription required}} {{closed access}}</ref> in particular [[DNA]]. Since then, they have become ubiquitous in the field of [[bioinformatics]].<ref name=durbin>{{Durbin 1998|mode=cs1}}</ref>