Forward–backward algorithm: Difference between revisions

Revision as of 23:44, 11 February 2009

Revision as of 04:53, 28 February 2009

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== Formal description==

The following description takes as its base matrices of probability values rather than probability distributions. We transform the probability distributions related to a given [[hidden Markov model]] into matrix notation as follows.

The transition probabilities <math>\mathbf{P}(X_t\mid X_{t-1})</math> of a given random variable <math>X_t</math> representing all possible states in the [[hidden Markov model]] will be represented by the matrix <math>\mathbf{T}</math> where the row index, i, will represent the start state and the column index, j, represents the target state. For example, in the example below <math>\mathbf{T}</math> would be defined as:

<math>\mathbf{T} = \begin{pmatrix}