Hidden Markov Models
Probabilis1c Graphical Models
Representa1on Template Models
Hidden Markov Models Daphne Koller
Hidden Markov Models S
S’
S0
O’
0.3
s1
s2
S2
S3
O1
O2
O3
0.1
0.5 0.7
S1
0.4 0.6
s3
0.5
s4
0.9 Daphne Koller
Numerous Applications • • • •
Robot localization Speech recognition Biological sequence analysis Text annotation
Daphne Koller
Robot Localization u
(0)
u
u
(1)
(t-1)
control signal robot pose
S(0)
S(1)
S(2)
o(1)
o(2)
...
S(t)
map sensor observation
o(t) Daphne Koller
Speech Recognition
Dan Jurafsky, Stanford
Daphne Koller
Segmentation of Acoustic Signal
Dan Jurafsky, Stanford
Daphne Koller
Phonetic Alphabet • • • • • • • • • • • • • •
AA AE AH AO AW AY B CH D DH EH ER EY F
odd at hut ought cow hide be cheese dee thee Ed hurt ate fee
AA D AE T HH AH T AO T K AW HH AY D B IY CH IY Z D IY DH IY EH D HH ER T EY T F IY
• • • • • • • • • • • •
•
G HH IH IY JH K L M N NG OW OY
P
green he it eat gee key lee me knee ping oat toy
pee
http://www.speech.cs.cmu.edu/cgi-bin/cmudict
G R IY N HH IY IH T IYT JH IY K IY L IY M IY N IY P IH NG OW T T OY
P IY
• • • • • • • • • • • •
R S SH T TH UH UW V W Y Z ZH
read sea she tea theta hood two vee we yield zee seizure
R IY D S IY SH IY T IY TH EY T AH HH UH D T UW V IY W IY Y IY L D Z IY S IY ZH ER
Daphne Koller
Word HMM
Dan Jurafsky, Stanford
Daphne Koller
Phone HMM
Dan Jurafsky, Stanford
Daphne Koller
Recognition HMM
Dan Jurafsky, Stanford
Daphne Koller
Summary • HMMs can be viewed as a subclass of DBNs • HMMs seem unstructured at the level of random variables • HMM structure typically manifests in sparsity and repeated elements within the transition matrix • HMMs are used in a wide variety of applications for modeling sequences Daphne Koller
Representa1on Template Models
Hidden Markov Models Daphne Koller
Hidden Markov Models S
S’
S0
O’
0.3
s1
s2
S2
S3
O1
O2
O3
0.1
0.5 0.7
S1
0.4 0.6
s3
0.5
s4
0.9 Daphne Koller
Numerous Applications • • • •
Robot localization Speech recognition Biological sequence analysis Text annotation
Daphne Koller
Robot Localization u
(0)
u
u
(1)
(t-1)
control signal robot pose
S(0)
S(1)
S(2)
o(1)
o(2)
...
S(t)
map sensor observation
o(t) Daphne Koller
Speech Recognition
Dan Jurafsky, Stanford
Daphne Koller
Segmentation of Acoustic Signal
Dan Jurafsky, Stanford
Daphne Koller
Phonetic Alphabet • • • • • • • • • • • • • •
AA AE AH AO AW AY B CH D DH EH ER EY F
odd at hut ought cow hide be cheese dee thee Ed hurt ate fee
AA D AE T HH AH T AO T K AW HH AY D B IY CH IY Z D IY DH IY EH D HH ER T EY T F IY
• • • • • • • • • • • •
•
G HH IH IY JH K L M N NG OW OY
P
green he it eat gee key lee me knee ping oat toy
pee
http://www.speech.cs.cmu.edu/cgi-bin/cmudict
G R IY N HH IY IH T IYT JH IY K IY L IY M IY N IY P IH NG OW T T OY
P IY
• • • • • • • • • • • •
R S SH T TH UH UW V W Y Z ZH
read sea she tea theta hood two vee we yield zee seizure
R IY D S IY SH IY T IY TH EY T AH HH UH D T UW V IY W IY Y IY L D Z IY S IY ZH ER
Daphne Koller
Word HMM
Dan Jurafsky, Stanford
Daphne Koller
Phone HMM
Dan Jurafsky, Stanford
Daphne Koller
Recognition HMM
Dan Jurafsky, Stanford
Daphne Koller
Summary • HMMs can be viewed as a subclass of DBNs • HMMs seem unstructured at the level of random variables • HMM structure typically manifests in sparsity and repeated elements within the transition matrix • HMMs are used in a wide variety of applications for modeling sequences Daphne Koller
