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Viterbi Training

• It is like Baum-Welsh. • Instead of the As and Es, the most probable paths for the training sequences are derived using the Viterbi algorithm.• Guaranteed to converge.• Maximize

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Baum-Welsh Example:

Generating model Estimated model from 300 rolls of dice

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Estimated model from 30000 rolls of dice

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Modeling with labeled sequences

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CML (conditional maximum likelihood)

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3.4 HMM model structure

• Fully connected model?– Never works in practice due to local maxima

• In practice, successful models are constructed based on knowledge about the problem

• If we set akl=0, in the Baum-Weltch estimation, akl will remain 0

• How to choose a model with our knowledge?

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Duration modeling

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Silent States

for 200 states, it requires 200*199/2

transitions

for 200 non-silent states, it requires

around 600 transitions

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For HMM without loops consisting entirely of silent states,all HMM algorithms in Section 3.2 and 3.3 could be extended.

For forward algorithm:

For HMM with loops consisting entirely of silent states,we could eliminate silent states by calculating the effectivetransition probabilities between real states in the model

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3.5 Higher Order Markov Chains

2nd-order Markov Chain

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13NORF: Non-coding Open Reading Frame

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Inhomogeneous Markov Chain

• Use three different Markov Chains to model coding regions

Pr(x) =

• n-th order emission probabilities

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• To avoid underflow error, two ways to deal with the problem– The log transformation

– Scaling of probabilities

3.6 Numerical stability of HMM algorithms

• The log transformation

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• Scaling of probabilities