Forward–backward algorithm

The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions o 1 : T := o 1 , … , o T {\displaystyle o_{1:T}:=o_{1},\dots ,o_{T}} , i.e. it computes, for all hidden state variables X t ∈ { X 1 , … , X T } {\displaystyle X_{t}\in \{X_{1},\dots ,X_{T}\}} , the distribution P ( X t | o 1 : T ) {\displaystyle P(X_{t}\ |\ o_{1:T})} .

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