Notice that this expression is
calculated from the
's
of the preceding time step and the
transition probabilites, and does not include the obervation
probability (unlike the calculation of the
's themselves).
This is because we want these
's
to answer the question `If I am
here, by what route is it most likely I arrived?' - this
question relates to the hidden states, and therefore confusing
factors due to the observations can be overlooked.
2e. Advantages of the approach
Using the Viterbi algorithm to decode an observation sequence
carries two important advantages:
There is a reduction in computational complexity by using
the recursion - this argument is exactly analogous to that
used in justifying the forward algorithm.
's
of the preceding time step and the
transition probabilites, and does not include the obervation
probability (unlike the calculation of the
's
to answer the question `If I am
here, by what route is it most likely I arrived?' - this
question relates to the hidden states, and therefore confusing
factors due to the observations can be overlooked.