Lyle Ungar, University of Pennsylvania Hidden Markov Models.

Lyle Ungar, University of Pennsylvania

Hidden Markov Hidden Markov ModelsModels

2Lyle H Ungar, University of Pennsylvania

Markov ModelMarkov ModelMarkov ModelMarkov Model

Sequence of states E..g., exon, intron, …

Sequence of observations E.g., AATCGGCGT Called “emissions”

Probability of transition The Markov matrix Mij = p(Sj | Si)

Probability of emission P(Ok|Sj)

3Lyle H Ungar, University of Pennsylvania

Markov Matrix propertiesMarkov Matrix propertiesMarkov Matrix propertiesMarkov 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) = Mij P(Si)

0.67 = 0.4 0.7 0.1

0.33 0.6 0.3 0.9

4Lyle H Ungar, University of Pennsylvania

Prokaryotic HMMProkaryotic HMMProkaryotic HMMProkaryotic HMM

5Lyle H Ungar, University of Pennsylvania

Eukarotic HMMEukarotic HMMEukarotic HMMEukarotic HMM

6Lyle H Ungar, University of Pennsylvania

Hidden Markov ModelHidden Markov ModelHidden Markov ModelHidden Markov Model

Can’t 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 programming “Viterbi algorithm”

7Lyle H Ungar, University of Pennsylvania

More Realistic HMMsMore Realistic HMMsMore Realistic HMMsMore Realistic HMMs

Frame Shifts need more states

Generalized HMMs (GMMs) Distribution of exon lengths is not

geometric

Example gene finders Genscan

8Lyle H Ungar, University of Pennsylvania

How well do they work?How well do they work?How well do they work?How well do they work?

Define criteria for working wellBase level, exon level or

entire gene?

Sn: Sensitivity = fraction of correct exons over actual exons

Sp: Specificity = fraction of correct exons over predicted exons

9Lyle H Ungar, University of Pennsylvania

HMM accuraciesHMM accuraciesHMM accuraciesHMM accuracies

http://www1.imim.es/courses/SeqAnalysis/GeneIdentification/Evaluation.html

10Lyle H Ungar, University of Pennsylvania

Combined methodsCombined methodsCombined methodsCombined methods

HMM plus sequence similarity Twinscan

11Lyle H Ungar, University of Pennsylvania

Align using an HMMAlign using an HMMAlign using an HMMAlign using an HMM

ACCGGA__TTTG__CGGACGTAT_DDMMMMIIMMMD

ACCGGA__TTTG__CGGACGTAT_DDMMMMIIMMMD

12Lyle H Ungar, University of Pennsylvania

Combined HMMCombined HMMCombined HMMCombined HMM