hidden markov models a first-order hidden markov model is completely defined by: a set of states. an...
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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)
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Linear Architecture
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Loop Architecture
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Wheel Architecture
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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.
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HMM APPLICATIONS
• MULTIPLE ALIGNMENTS
• DATA BASE SEARCHES AND
DISCRIMINATION/CLASSIFICATION
• STRUCTURAL ANALYSIS AND
PATTERN DISCOVERY
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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.
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HMMs of Protein Families
• Globins
• Immunoglobulins
• Kinases
• G-Protein-Coupled Receptors
• Pfam is a data base of protein domains
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HMMs of DNA
• coding/non-coding regions (E. Coli)
• exons/introns/acceptor sites
• promoter regions
• gene finding
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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
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IG MODEL ENTROPY
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IG EMISSIONS
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IG Viterbi Path
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IG MULTIPLE ALIGNMENT
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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.
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GPCR ENTROPY
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GPCR HYDROPATHY
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GPCR Model Structure
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GPCR SCORING
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PROMOTER ENTROPY
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PROMOTER BENDABILITY
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PROMOTER PROPELLER TWIST
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SOFTWARE STRUCTURE
• OBJECT-ORIENTED LIBRARY FOR MACHINE LEARNING
• ENGINE IN C++
• GRAPHICAL USER INTERFACE IN JAVA
• RUNS UNDER WINDOWS NT AND UNIX (SOLARIS, IRIX)
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INFORMATION
• ADDITIONAL INFORMATION, POINTERS, REFERENCES, AND SOFTWARE DOWNLOAD:
WWW.NETID.COM