Finding the Most Likely Parse for a Sentence
The algorithm works by finding the highest probability partial parse tree spanning a certain substring that is rooted with a certain nonterminal.
?i(p,q) = the highest inside probability parse of a subtree Npqi
Initialization: ?i(p,p) = P(Ni --> wp)
Induction: ?i(p,q) = max1?j,k?n,p?r<qP(Ni --> Nj Nk) ?j(p,r) ?k(r+1,q)
Store backtrace: ?i(p,q)=argmax(j,k,r)P(Ni --> Nj Nk) ?j(p,r) ?k(r+1,q)
Termination: P(t^)= ?1(1,m)