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Properly reconstruct sequence of states in Viterbi algorithm #4

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@olvb olvb commented Sep 14, 2022

Hi, thanks a lot for the tutorial, I found it very intuitive.

However there is a mistake at the end of the part concerning the Viterbi algorithm. It is not possible to simply select the state with highest probability at each step. Doing this will not reconstruct properly the sequence that lead to the most likely final state.

Instead, we have to memorize all the best intermediate states and how they connect to each other. Then when we have selected our final state, we just have to "backtrack" the series of states that lead to it.

Olivier Birot added 7 commits September 14, 2022 15:13
…bability

In a latter commit, we will add additional instructions in each branch
to track the sequence of intermediate states.
We will need to disambiguate between a single weather state and a list
of weather states in a latter commit.
Before this commit we were just selecting the state with max probability
at each time step, but this would not properly rebuild the sequence of
states leading to the final most likely state.

Note that this changes the result.
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