Revision as of 18:17, 6 August 2019 edit Pauli133 (talk \| contribs) Extended confirmed users 29,364 edits m this is a horrendous citation format, but at least we can keep it from generating lint errors... ← Previous edit		Revision as of 08:10, 26 November 2019 edit undo 136.25.185.15 (talk) →Forward probabilities: i usually refers to the row vector index, and j the column vector index. the previous i, j convention did not agree with the convention used on the baum-welch alg wiki page, which references this page Next edit →
Line 26: 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 column index <math>ij</math> will represent the target state and the row index <math>ji</math> represents the start state. A transition from row-vector state <math>\mathbf{\pi_t}</math> to the incremental row-vector state <math>\mathbf{\pi_{t+1}}</math> is written as <math>\mathbf{\pi_{t+1}} = \mathbf{\pi_{t}} \mathbf{T}</math>. The example below represents a system where the probability of staying in the same state after each step is 70% and the probability of transitioning to the other state is 30%. The transition matrix is then: :<math>\mathbf{T} = \begin{pmatrix}

Forward–backward algorithm: Difference between revisions