The Probability of a String II: Using Outside Probabilities
We use the Outside Algorithm based on the outside probabilities: P(w1m|G)=?j?j(k,k)P(Nj --> wk)
Base Case: ?1(1,m)= 1; ?j(1,m)=0 for j?1
Inductive Case: ?j(p,q)= <See book on pp. 395-396>.
Similarly to the HMM, we can combine the inside and the outside probabilities: P(w1m, Npq|G)= ?j ?j(p,q) ?j(p,q)