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Unformatted text preview: lattice” although it
should not be confused with a Birkhoﬀstyle lattice in mathematics
(which is quite diﬀerent). Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 522 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Trellis/Lattice/Grid We’ll see that it is very useful to view the HMM statespace as a
trellis.
It is sometimes called an HMM grid, or even a “lattice” although it
should not be confused with a Birkhoﬀstyle lattice in mathematics
(which is quite diﬀerent).
Key thing about a trellis representation is that it shows the Markov
transition matrix but time is also explicitly represented. Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 522 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Trellis/Lattice/Grid We’ll see that it is very useful to view the HMM statespace as a
trellis.
It is sometimes called an HMM grid, or even a “lattice” although it
should not be confused with a Birkhoﬀstyle lattice in mathematics
(which is quite diﬀerent).
Key thing about a trellis representation is that it shows the Markov
transition matrix but time is also explicitly represented.
Lets say there are DQ  = N states and T time steps. Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 522 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Trellis/Lattice/Grid We’ll see that it is very useful to view the HMM statespace as a
trellis.
It is sometimes called an HMM grid, or even a “lattice” although it
should not be confused with a Birkhoﬀstyle lattice in mathematics
(which is quite diﬀerent).
Key thing about a trellis representation is that it shows the Markov
transition matrix but time is also explicitly represented.
Lets say there are DQ  = N states and T time steps.
Then the trellis is an (often rectangular) N × T grid. Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 522 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch A trellis for words things
all bright
great creatures beautiful
and wise small
wonderful A trellis really corresponds to a language — any string generated by the
trellis corresponds to a sentence in the language.
Note that the language “words” are listed on the edges. Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 523 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch A trellis for peptides Lattice
Points Lattice
Links List of peptides AQ
S HQ MP MPRAI
LL
AD FQMDE C EM STGH ST ACDE QR ST ACDEEMQRSTGHFQMDE
ACDEEMQRSTMPRAIFQMDE
ACDEEMQRSTLLADSTCFQMDE
ACDEAQSMPHQMPRAIFQMDE
ACDEAQSMPHQLLADSTCFQMDE
ACDEAQSAFQWMRSTCFQMDE AFQWMR Lattice (a partial ordering of peptide
subsegments) for the strings on the left. Peptides are fragments of proteins. Lattices can be used for this too. Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 524 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Markov T...
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 Winter '14

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