Copyright (c) 2002 by SNU CSE Biointe lligence Lab 1 Chap. 4 Pairwise alignment u Chap. 4 Pairwise alignment u sing HMMs sing HMMs Biointelligence Laboratory School of Computer Sci. & Eng. Seoul National University Seoul 151-742, Korea This slide file is available online at http://bi. snu .ac. kr /
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Copyright (c) 2002 by SNU CSE Biointelligence Lab 1 Chap. 4 Pairwise alignment using HMMs Biointelligence Laboratory School of Computer Sci. & Eng. Seoul.
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Copyright (c) 2002 by SNU CSE Biointelligence Lab 1
Chap. 4 Pairwise alignment using HMMsChap. 4 Pairwise alignment using HMMs
Biointelligence Laboratory
School of Computer Sci. & Eng.
Seoul National University
Seoul 151-742, Korea
This slide file is available online at
http://bi.snu.ac.kr/
2Copyright (c) 2002 by SNU CSE Biointelligence Lab
ContentsContents
FSA → HMM Pair HMMs The full probability of x & y Suboptimal alignment posterior that xi is aligned to yi
Pair HMMs vs FSAs for searching
3Copyright (c) 2002 by SNU CSE Biointelligence Lab
Figure 4.1 A finite state machine diagram for affine gap alignment on the left, and the corresponding probabilistic model on the right.
X(+1,+0)
M(+1,+1)
Y(+0,+1)
-e
-d
-d
-es(xi,yj)
s(xi,yj)
s(xi,yj)
Xqxi
Mpxiyj
Yqyj
ε
ε1-ε
1-ε
δ
δ
1-δ
4Copyright (c) 2002 by SNU CSE Biointelligence Lab
Recurrence RelationRecurrence Relation
ejiV
djiVjiV
ejiV
djiVjiV
jiV
jiV
jiV
yxsjiV ii
)1,(
)1,(max),(
),1(
),1(max),(
)1,1(
)1,1(
)1,1(
max),(),(
Y
MY
X
MX
Y
X
M
M
5Copyright (c) 2002 by SNU CSE Biointelligence Lab
Pair HMMs (1)Pair HMMs (1)
FSA → HMMs: How to? Specification of emission & transition probabilities
X(+1,+0)
M(+1,+1)
Y(+0,+1)
-e
-d
-d
-es(xi,yj)
s(xi,yj)
s(xi,yj)
Xqxi
Mpxiyj
Yqyj
ε
ε1-ε
1-ε
δ
δ
1-δ
6Copyright (c) 2002 by SNU CSE Biointelligence Lab
Pair HMMs (2)Pair HMMs (2)
Definition of begin state & end state Providing pd. over all possible sequences
Pair HMM Identical to ordinary HMM Emitting a pairwise alignment
7Copyright (c) 2002 by SNU CSE Biointelligence Lab
Xqxi
Mpxiyj
Y
qyj
ε
ε
1-ε-τ
δ
δ1-2δ-τ
1-ε-τ
δ
δ
τ
τ
τ
τ
BeginEnd
Figure 4.2 The full probabilistic version of Figure 4.1
1-2δ-τ
8Copyright (c) 2002 by SNU CSE Biointelligence Lab
Pair HMMs (3)Pair HMMs (3)
Algorithm: Viterbi algorithm for pair HMMs Initialization: