From PRGs to PCFGs
In the HMM, we were able to efficiently do calculations in terms of forward and backward probabilities.
In a parse tree, the forward probability corresponds to everything above and including a certain node, while the backward probability corresponds to the probability of everything below a certain node.
We introduce Outside (?j ) and Inside (?j) Probs.:
- ?j(p,q)=P(w1(p-1) , Npqj,w(q+1)m|G)
- ?j(p,q)=P(wpq|Npqj, G)