# Prof je bilmes ee596awinter 2013dgms lecture 5 jan

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Unformatted text preview: lattice” although it should not be confused with a Birkhoﬀ-style lattice in mathematics (which is quite diﬀerent). Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-22 (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 state-space as a trellis. It is sometimes called an HMM grid, or even a “lattice” although it should not be confused with a Birkhoﬀ-style 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 5-22 (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 state-space as a trellis. It is sometimes called an HMM grid, or even a “lattice” although it should not be confused with a Birkhoﬀ-style 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 5-22 (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 state-space as a trellis. It is sometimes called an HMM grid, or even a “lattice” although it should not be confused with a Birkhoﬀ-style 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 5-22 (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 5-23 (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 sub-segments) 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 5-24 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Markov T...
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## This document was uploaded on 04/05/2014.

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