  The inside-outside probabilities are typically used for reestimating
Probabilistic Context Free Grammars (PCFGs), just as the forward-backward
probabilities are typically used for reestimating HMMs. I show several novel
uses, including improving parser accuracy by matching parsing algorithms to
evaluation criteria; speeding up DOP parsing by 500 times; and 30 times faster
PCFG thresholding at a given accuracy level. I also give an elegant,
state-of-the-art grammar formalism, which can be used to compute inside-outside
probabilities; and a parser description formalism, which makes it easy to
derive inside-outside formulas and many others.
