Forward–backward algorithm: Difference between revisions

Revision as of 13:25, 21 October 2020

Revision as of 22:01, 4 November 2020

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:<math>\mathbf{P}(O = j)=\sum_{i} \pi_i B_{i,j}</math>

ThisThe probability of a given state leading to the observed event j can be represented in matrix form by multiplying the state row-vector (<math>\mathbf{\pi}</math>) bywith an observation matrix (<math>\mathbf{O_j} = \mathrm{diag}(B_{*,o_j})</math>) containing only diagonal entries. Each entry is the probability of the observed event given each state. Continuing the above example, anthe observation ofmatrix for event 1 would be:

:<math>\mathbf{O_1} = \begin{pmatrix}