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Hidden Markov Models

Hidden Markov Models. A first-order Hidden Markov Model is completely defined by: A set of states. An alphabet of symbols. A transition probability matrix T=(t ij ) An emission probability matrix E=(e iX ). Linear Architecture. Loop Architecture. Wheel Architecture. Basic Ideas.

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Hidden Markov Models

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  1. Hidden Markov Models A first-order Hidden Markov Model is completely defined by: • A set of states. • An alphabet of symbols. • A transition probability matrix T=(tij) • An emission probability matrix E=(eiX)

  2. Linear Architecture

  3. Loop Architecture

  4. Wheel Architecture

  5. Basic Ideas • As in speech recognition, use Hidden Markov Models (HMM) to model a family of related primary sequences. • As in speech recognition, in general use a left to right HMM: once the system leaves a state it can never reenter it. The basic architecture consists of a main backbone chain of main states, and two side chains of insert and delete states. • The parameters of the model are the transition and emission probabilities. These parameters are adjusted during training from examples. • After learning, the model can be used in a variety of tasks including: multiple alignments, detection of motifs, classification, data base searches.

  6. HMM APPLICATIONS • MULTIPLE ALIGNMENTS • DATA BASE SEARCHES AND DISCRIMINATION/CLASSIFICATION • STRUCTURAL ANALYSIS AND PATTERN DISCOVERY

  7. Multiple Alignments • No precise definition of what a good alignment is (low entropy, detection of motifs). • The multiple alignment problem is NP complete (finding longest subsequence). • Pairwise alignment can be solved efficiently by dynamic programming in O(N2) steps. • For K sequences of average length N, dynamic programming scales like O(NK), exponentially in the number of sequences. • Problem of variable scores and gap penalties.

  8. HMMs of Protein Families • Globins • Immunoglobulins • Kinases • G-Protein-Coupled Receptors • Pfam is a data base of protein domains

  9. HMMs of DNA • coding/non-coding regions (E. Coli) • exons/introns/acceptor sites • promoter regions • gene finding

  10. IMMUNOGLOBULINS • 294 sequences (V regions) with minimum length 90, average length 117, and maximal length 254 • linear model of length 117 trained with a random subset of 150 sequences

  11. IG MODEL ENTROPY

  12. IG EMISSIONS

  13. IG Viterbi Path

  14. IG MULTIPLE ALIGNMENT

  15. G-PROTEIN-COUPLED RECEPTORS • 145 sequences with minimum length 310, average length 430, and maximal length 764. • Model trained with 143 sequences (3 sequences contained undefined symbols) using Viterbi learning.

  16. GPCR ENTROPY

  17. GPCR HYDROPATHY

  18. GPCR Model Structure

  19. GPCR SCORING

  20. PROMOTER ENTROPY

  21. PROMOTER BENDABILITY

  22. PROMOTER PROPELLER TWIST

  23. SOFTWARE STRUCTURE • OBJECT-ORIENTED LIBRARY FOR MACHINE LEARNING • ENGINE IN C++ • GRAPHICAL USER INTERFACE IN JAVA • RUNS UNDER WINDOWS NT AND UNIX (SOLARIS, IRIX)

  24. INFORMATION • ADDITIONAL INFORMATION, POINTERS, REFERENCES, AND SOFTWARE DOWNLOAD: WWW.NETID.COM

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