Forward–backward algorithm: Difference between revisions

Revision as of 19:03, 22 February 2019

Revision as of 12:28, 6 August 2019

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We can now make this general procedure specific to our series of observations. Assuming an initial state vector <math>\mathbf{\pi_0}</math>, (which can be optimized as a parameter through repetitions of the forward-back procedure), we begin with <math>\mathbf{f_{0:0}} = \mathbf{\pi_0}</math>, then updating the state distribution and weighting by the likelihood of the first observation:

:<math>

\mathbf{f_{0:01}} = \mathbf{\pi_0} \mathbf{T} \mathbf{O_{o(01)}}

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