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HMM (Hidden Markov Model)

Date post: 29-Jun-2015
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2. HIDDEN MARKOV MODEL(HMM) Real-world has structures and processes which have observable outputs. Usually sequential . Cannot see the event producing the output. Problem: how to construct a model of the structure or process given only observations. 3. HISTORY OF HMM Basic theory developed and published in 1960s and 70s No widespread understanding and application until late 80s Why? Theory published in mathematic journals which were not widely read. Insufficient tutorial material for readers to understand and apply concepts. 4. Andrei Andreyevich Markov 1856-1922Andrey Andreyevich Markov was a Russian mathematician. He is best known for his work on stochastic processes. A primary subject of his research later became known as Markov chains and Markov processes . 5. HIDDEN MARKOV MODEL A Hidden Markov Model (HMM) is a statical model in which the system is being modeled is assumed to be a Markov process with hidden states. Markov chain property: probability of each subsequent state depends only on what was the previous state. 6. EXAMPLE OF HMM Coin toss: Heads, tails sequence with 2 coins You are in a room, with a wall Person behind wall flips coin, tells result Coin selection and toss is hidden Cannot observe events, only output (heads, tails) from events Problem is then to build a model to explain observed sequence of heads and tails. 7. EXAMPLE OF HMM Weather Once each day weather is observed State 1: rain State 2: cloudy State 3: sunny What is the probability the weather for the next 7 days will be: sun, sun, rain, rain, sun, cloudy, sun Each state corresponds to a physical observable event 8. HMM COMPONENTS A set of states (xs) A set of possible output symbols (ys) A state transition matrix (as) probability of making transition from one state to the next Output emission matrix (bs) probability of a emitting/observing a symbol at a particular state Initial probability vector probability of starting at a particular state Not shown, sometimes assumed to be 1 9. EXAMPLE OF HMM 0.30.7RainDry 0.2 Two states : Rain and Dry. Transition probabilities: P(Rain|Rain)=0.3 ,P(Dry|Rain)=0.7 , P(Ra)=0.6 . in|Dry)=0.2, P(Dry|Dry)=0.8 Initial probabilities: say P(Rain)=0.4 , P(Dry0.8 10. CALCULATION OF HMM 11. HMM COMPONENTS 12. COMMON HMM TYPES Ergodic (fully connected): Every state of model can be reached in a single step from every other state of the model. Bakis (left-right): As time increases, states proceed from left to right 13. HMM IN BIOINFORMATICS Hidden Markov Models (HMMs) are a probabilistic model for modeling and representing biological sequences. They allow us to do things like find genes, do sequence alignments and find regulatory elements such as promoters in a principled manner. 14. PROBLEMS OF HMM Three problems must be solved for HMMs to be useful in real-world applications 1) Evaluation2) Decoding3) Learning 15. EVOLUTION OF PROBLEM Given a set of HMMs, which is the one most likely to have produced the observation sequence? GACGAAACCCTGTCTCTATTTATCC p(HMM-3)? p(HMM-1)? p(HMM-2)? HMM 1HMM 2HMM 3p(HMM-n)?HMM n 16. DECODING PROBLEM 17. TRAINING PROBLEMFrom raw seqence data AATAGAGAGGTTCGACTCTGCAT TTCCCAAATACGTAATGCTTACGG TACACGACCCAAGCTCTCTGCTT GAATCCCAAATCTGAGCGGACAG ATGAGGGGGCGCAGAGGAAAAA CAGGTTTTGGACCCTACATAAAN AGAGAGGTTCGTAAATAGAGAGG TTCGACTCTGCATTTCCCAAATAC GTAATGCTTACGGTTAAATAGAGA GGTTCGACTCTGCATTTCCCAAA TACGTAATGCTTACGGTACACGA CCCAAGCTCTCTGCTTGTAACTT GTTTTNGTCGCAGCTGGTCTTGC CTTTGCTGGGGCTGCTGACto Transition Probabilities A+ C+A+H o w ?C+ G+ T+ ACGT-0.17 0.16 0.15 0.07 0.01 0.01 0.01 0.010.26 0.36 0.33 0.35 0.01 0.01 0.01 0.01G+ T+0.42 0.26 0.37 0.37 0.01 0.01 0.01 0.010.11 0.18 0.11 0.17 0.01 0.01 0.01 0.01A-C-G-T-0.01 0.01 0.01 0.01 0.29 0.31 0.24 0.170.01 0.01 0.01 0.01 0.2 0.29 0.23 0.230.01 0.01 0.01 0.01 0.27 0.07 0.29 0.280.01 0.01 0.01 0.01 0.2 0.29 0.2 0.28 18. HMM-APPLICATION DNA Sequence analysis Protein family profiling Predprediction Splicing signals prediction Prediction of genes Horizontal gene transfer Radiation hybrid mapping, linkage analysis Prediction of DNA functional sites. CpG island 19. HMM-APPLICATION Speech Recognition Vehicle Trajectory Projection Gesture Learning for Human-Robot Interface Positron Emission Tomography (PET) Optical Signal Detection Digital Communications Music Analysis 20. HMM-BASED TOOLS GENSCAN (Burge 1997) FGENESH (Solovyev 1997) HMMgene (Krogh 1997) GENIE (Kulp 1996) GENMARK (Borodovsky & McIninch 1993) VEIL (Henderson, Salzberg, & Fasman 1997) 21. BIOINFORMATICS RESOURCES PROBE www.ncbi.nlm.nih.gov/ BLOCKS www.blocks.fhcrc.org/ META-MEME www.cse.ucsd.edu/users/bgrundy/metameme.1.0.html SAM www.cse.ucsc.edu/research/compbio/sam.html HMMERS hmmer.wustl.edu/ HMMpro www.netid.com/ GENEWISE www.sanger.ac.uk/Software/Wise2/ PSI-BLAST www.ncbi.nlm.nih.gov/BLAST/newblast.html PFAM www.sanger.ac.uk/Pfam/ 22. Refrences Rabiner, L. R. (1989). A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE, 77(2), 257-285. Essential bioinformatics, Jin Xion http://www.sociable1.com/v/Andrey-Markov108362562522144#sthash.tbdud7my.dpuf 23. Thank You!