1. Hidden Markov Models Baldomero Oliva Miguel UniversitatPompeuFabra A = a 1 a 2 a 3 a 4 a 5 B = b 1 b 2 b 3 b 4 b 5 C = c 1 c 2 c 3 c 4 c 5 D = d 1 d 2 d 3 d 4 d 5 E = e 1 e 2 e 3 e 4 e 5 P1P2P3P4P5P1P2P3P4P5 P 1 (c 1 )P 2 (c 2 )P 3 (c 3 )P 4 (c 4 )P 5 (c 5 ) = P total

2. Bayesian Inference H M = { set of events derived from a model} Bayes theorem: P( M|D) = P(D) P(D|M) P(M) H D = { corpus of known data} Baldomero Oliva Miguel UniversitatPompeuFabra

3. UniversitatPompeuFabra likelihoodposterior Maximum a posteriori MAP Maximum likelihood ML Minimizar F= - log(P(D|M)) -log(P(M)) Minimizar F= - log(P(D|M)) Bajo condiciones de contorno i (M) =0

4. Baldomero Oliva Miguel UniversitatPompeuFabra

5. e HMMHMM A A G G C C G G T T p e (A)p e (G)..... Baldomero Oliva Miguel UniversitatPompeuFabra

6. ..... AGCGT e p e (A)p e (G)..... i A A C G AACG p i (A) T ei Baldomero Oliva Miguel UniversitatPompeuFabra HMMHMM

7. AGCGT e p e (A)p e (G)..... d i AACG-- p i (A)..... T ei T id Baldomero Oliva Miguel UniversitatPompeuFabra HMMHMM

8. e d i { P e } { P i } { T ab } Baldomero Oliva Miguel UniversitatPompeuFabra

9. e d i start e d i e d i end Architecture HMM Baldomero Oliva Miguel UniversitatPompeuFabra P(Sequence, path|model) = Product

10. Baldomero Oliva Miguel UniversitatPompeuFabra A posteriori { P e ; P i } state i DATA sequence path

11. e d i start e d i e d i end Baldomero Oliva Miguel UniversitatPompeuFabra Boundary conditions

12. Baldomero Oliva Miguel UniversitatPompeuFabra

13. UniversitatPompeuFabra e d i..T....S....T....Y.. e Thr X =3/5 e Pro X =0/5 Dirichlet

14. Baldomero Oliva Miguel UniversitatPompeuFabra

15. UniversitatPompeuFabra INFORMATION