modele markov ascunse markov ascunse.pdf- o stare ascunsa (pe care nu o vad, ci o pot infera), x t...
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![Page 1: Modele Markov Ascunse Markov Ascunse.pdf- o stare ascunsa (pe care nu o vad, ci o pot infera), X t Am date: - un set de astfel de observatii, Y 1:t - probabilitatile initiale ale starilor](https://reader035.vdocuments.pub/reader035/viewer/2022071608/614683be7599b83a5f004579/html5/thumbnails/1.jpg)
Modele Markov Ascunse
Laura Florea
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Date
La un moment de timp, t, am:
- o observatie, Yt- o stare ascunsa (pe care nu o vad, ci o pot infera), Xt
Am date:
- un set de astfel de observatii, Y1:t
- probabilitatile initiale ale starilor ascunse, P(X0)
- probabilitatile de emisie a observatiei curente din fiecare stare ascunsa, P(Yt|Xt), pentru orice t
- probabilitatile de trecere dintr-o stare ascunsa in altastare ascunsa, P(Xt|Xt-1)
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Scop
• Avand un set de observatii, care esteprobabilitatea ca starea ascunsa in care ma aflu sa fie Xt , P(Xt|Y1:t)
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Algoritm: predictie
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Am folosit:
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![Page 5: Modele Markov Ascunse Markov Ascunse.pdf- o stare ascunsa (pe care nu o vad, ci o pot infera), X t Am date: - un set de astfel de observatii, Y 1:t - probabilitatile initiale ale starilor](https://reader035.vdocuments.pub/reader035/viewer/2022071608/614683be7599b83a5f004579/html5/thumbnails/5.jpg)
Algoritm: predictie
Starea ascunsa actuala:- depinde doar de starea ascunsa trecuta si de observatia actuala. - NU depinde de observatiile trecute.
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![Page 6: Modele Markov Ascunse Markov Ascunse.pdf- o stare ascunsa (pe care nu o vad, ci o pot infera), X t Am date: - un set de astfel de observatii, Y 1:t - probabilitatile initiale ale starilor](https://reader035.vdocuments.pub/reader035/viewer/2022071608/614683be7599b83a5f004579/html5/thumbnails/6.jpg)
Algoritm: update Bayesian
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Am folosit:
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![Page 7: Modele Markov Ascunse Markov Ascunse.pdf- o stare ascunsa (pe care nu o vad, ci o pot infera), X t Am date: - un set de astfel de observatii, Y 1:t - probabilitatile initiale ale starilor](https://reader035.vdocuments.pub/reader035/viewer/2022071608/614683be7599b83a5f004579/html5/thumbnails/7.jpg)
Algoritm: update Bayesian
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Dar observatia curenta depinde doar de starea curenta. NU depinde de observatiile anterioare.
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![Page 8: Modele Markov Ascunse Markov Ascunse.pdf- o stare ascunsa (pe care nu o vad, ci o pot infera), X t Am date: - un set de astfel de observatii, Y 1:t - probabilitatile initiale ale starilor](https://reader035.vdocuments.pub/reader035/viewer/2022071608/614683be7599b83a5f004579/html5/thumbnails/8.jpg)
Algoritm: update Bayesian
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CunoscutaCalculata la
pasul anterior
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Exemplu preluat de la Luis Serrano, A friendly introduction to Bayes Theorem and Hidden Markov Modelshttps://www.youtube.com/watch?v=kqSzLo9fenk
Observatii
Stariascunse
Exemplu
![Page 10: Modele Markov Ascunse Markov Ascunse.pdf- o stare ascunsa (pe care nu o vad, ci o pot infera), X t Am date: - un set de astfel de observatii, Y 1:t - probabilitatile initiale ale starilor](https://reader035.vdocuments.pub/reader035/viewer/2022071608/614683be7599b83a5f004579/html5/thumbnails/10.jpg)
Probabilitati de emisie
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Probabilitati de tranzitie
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Date
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Cum aflu probabilitatile?
Prin masuratori anterioare (antrenare)
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Cum aflu probabilitatile?
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Cum aflu probabilitatile?
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Daca nu stie decat probabilitatileinitiale…
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Daca stie si observatia actuala
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Daca stie si observatia actuala
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O singura observatie: 2 cazuri posibile
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Se stiu:
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Am doua observatii
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Exista 4 cazuri
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Calculez pentru fiecare probabilitatea:
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Si aleg varianta de maxima verosimilitate
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Am 3 observatii:
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Am 23=8 posibilitati
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Calculez pentru fiecare probabilitatea:
![Page 32: Modele Markov Ascunse Markov Ascunse.pdf- o stare ascunsa (pe care nu o vad, ci o pot infera), X t Am date: - un set de astfel de observatii, Y 1:t - probabilitatile initiale ale starilor](https://reader035.vdocuments.pub/reader035/viewer/2022071608/614683be7599b83a5f004579/html5/thumbnails/32.jpg)
Si aleg varianta de maxima verosimilitate
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……
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Algoritmul Viterbi
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Algoritmul Viterbi
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Algoritmul Viterbi
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Algoritmul Viterbi
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Algoritmul Viterbi
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Algoritmul Viterbi
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Algoritmul Viterbi
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Algoritmul Viterbi
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Algoritmul Viterbi
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Algoritmul Viterbi
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Algoritmul Viterbi
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Algoritmul Viterbi