Viterbi: Backward Pass

Course Q&A Natural Language Processing NLP with Probabilistic Models
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Kindly explain this to me:
argmax Ci5 = 3 (OK, understood, as 0.01 is max among others)
argmax Ci4 = 1 (OK, understood, as 0.02 is max among others)
argmax Ci3 = 3 (NOT-understood, as 0.05 is max among others, shouldn’t be argmax Ci3 = 2)
argmax Ci2 = 2 (NOT-understood, as 0.125 is max among others, shouldn’t be argmax Ci2 = 1)

Kindly correct me, I am confused…

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Hi @Sagir_Mehmood

Here is a similar question.

What you confuse is that D matrix represent the path you traveled. The C matrix represent the best probability for that state (t_i) for that word (w_i) (in other, words for all paths). While the D matrix represent how you arrive at that probability.

So, w_5 value is taken from the C matrix, while other values are taken from the D matrix:

  • word w_5 best tag is t_1 because the biggest value in C is 0.01 (for t_1)
  • word w_4 best tag is t_3 because D matrix at (w_5, t_1) indicates 3
  • word w_3 best tag is t_1 because D matrix at (w_4, t_3) indicates 1
  • word w_2 best tag is t_3 because D matrix at (w_3, t_1) indicates 3
  • word w_1 best tag is t_2 because D matrix at (w_2, t_3) indicates 2
  • word <s> best tag is 0 because D matrix at (w_1, t_2) indicates 0

Cheers

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Thank you, it helped me a lot.