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Unformatted text preview: πi = k in the state path π), normalized by the
sum over all possible state paths. In our toy
model, this is just one state path in the
numerator and a sum over 14 state paths in
the denominator. We get a probability of
46% that the bestscoring fifth G is correct
and 28% that the sixth G position is correct
(Fig. 1, bottom). This is called posterior
decoding. For larger problems, posterior
decoding uses two dynamic programming
algorithms called Forward and Backward,
which are essentially like Viterbi, but they
sum over possible paths instead of choosing
the best.
Making more realistic models
Making an HMM means specifying four
things: (i) the symbol alphabet, K different
symbols (e.g., ACGT, K = 4); (ii) the number
of states in the model, M; (iii) emission
probabilities ei(x) for each state i, that sum
to one over K symbols x, Σ ei(x) = 1; and
x (iv) transition probabilities ti( j ) for each state
i going to any other state j (including itself)
that sum to one over the M states j, Σ ti( j ) = 1. For example, in our toy splicesite model,
maybe we’re not happy with our d...
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This note was uploaded on 04/06/2010 for the course COMPUTER S COSC1520 taught by Professor Paul during the Spring '09 term at York University.
 Spring '09
 PAUL

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