Markov Hidden Models
Lyle Ungar, University of Pennsylvania
Markov Model
Sequence
of states of observations of transition of emission
E..g., exon, intron, E.g., AATCGGCGT Called emissions The Markov matrix Mij = p(Sj | Si) P(Ok|Sj)
Sequence
Probability
Probability
Lyle H Ungar, University of Pennsylvania
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Markov Matrix properties
Columns
of M sum to one
You must transition somewhere
Multiplying
by M gives probilites of the state of the next item in the sequence P(Sj) 0.67 0.33 = = Mij P(Si) 0.4 0.7 0.1 0.6 0.3 0.9
Lyle H Ungar, University of Pennsylvania
3
Prokaryotic HMM
Lyle H Ungar, University of Pennsylvania
4
Eukarotic HMM
Lyle H Ungar, University of Pennsylvania
5
Hidden Markov Model
Cant
observe the states Need to estimate using HMM using an EM algorithm
Baum-Welsh or forward-backward
Given
an HMM, for a new sequence, find the most likely states
Done using dynamic Viterbi programming algorithm
Lyle H Ungar, University of Pennsylvania
6
More Realistic HMMs
Frame
Shifts HMMs (GMMs)
need more states Distribution of exon lengths is not geometric
Generalized
Example
gene finders
Genscan
Lyle H Ungar, University of Pennsylvania
7
How well do they work?
Define criteria for working well Base level, exon level or entire gene? Sn: Sensitivity = fraction of correct exons over actual exons Sp: Specificity = fraction of correct exons over predicted exons
Lyle H Ungar, University of Pennsylvania 8
HMM accura...