HMM在生物信息中的应用2.pptVIP

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HMM在生物信息中的应用2.ppt

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HMMs及其应用Hidden Markov Models Its Application Lecture # 11 Four Basic Problems for HMMs Determine the structure/topology of the HMM—states and transitions Determine the values of the model parameters—emission and transition probabilities (the learning problem). That is, how to adjust the model parameters to maximize P(O | m)? Given an observation sequence O = O1O2O3…Ot, and a model m = (T, E, ?), how to evaluate the probability of this sequence given the model (the estimation problem). That is, how to efficiently compute P(O | m)? Given an observation sequence O and a model m, how to find the most likely path through the model for the sequence (the decoding problem). That is, how to choose a corresponding state sequence Q = q1q2q3…qt which is optimal in some meaningful sense? About the Estimation Problem:Determining how probable an observed sequence is, given a model Basic Mathematics Markov chains: prob. of a sequence: S=a1a2...an P(S)=? Basic Mathematics Markov chains: prob. of a sequence: S=a1a2...an P(S)=P(a1)P(a2| a1)P(a3 | a1 a2)...P(an|a1... an-1) P(S)=P(a1)P(a2| a1)P(a3 | a2)...P(an|an-1) P(S)=P(a1) ? P(ai|ai-1) Basic Mathematics Markov chains: prob. of a sequence: S=a1a2...an P(S)=P(a1)P(a2| a1)P(a3 | a1 a2)...P(an|a1... an-1) P(S)=P(a1)P(a2| a1)P(a3 | a2)...P(an|an-1) P(S)=P(a1) ? P(ai|ai-1) HMMs: P(S) =? Basic Mathematics Markov chains: prob. of a sequence: S=a1a2...an P(S)=P(a1)P(a2| a1)P(a3 | a1 a2)...P(an|a1... an-1) P(S)=P(a1)P(a2| a1)P(a3 | a2)...P(an|an-1) P(S)=P(a1) ? P(ai|ai-1) HMMs: P(S) depends on states passed thru Basic Mathematics Markov chains: prob. of a sequence: S=a1a2...an P(S)=P(a1)P(a2| a1)P(a3 | a1 a2)...P(an|a1... an-1) P(S)=P(a1)P(a2| a1)P(a3 | a2)...P(an|an-1) P(S)=P(a1) ? P(ai|ai-1) HMMs: P(S) depends on states passed thru if known: (states= s1, s2... sn) P(S) = ? Basic Mathematics Markov chains: prob. of a sequence: S=a1a2...an P(S)=P(a1)P(a2| a1)P(a3 | a1 a2)...P(an|a1... an-1) P(S)=P(a1)P(a2| a1)P(a3 | a2)...P(an|an-1) P