 
Summary: Reliability
Steven Abney
Universitšat Tšubingen
The usual approach to stochastic parsing is to `reverse' a model of stochastic
generation. For example, a stochastic contextfree grammar (SCFG) G defines a
stochastic process for generating sentences. A stochastic choice is made at each
derivation step, and the probability P(d) of the derivation is the joint probability
of the stochastic choices made. P(d, x), the probability of producing derivation
d and in the process deriving sentence x, is P(d) if d is in fact a derivation of
x, and 0 otherwise. P(x) is d P(d, x). To parse a sentence x, we choose that
derivation d for which the conditional probability P(dx) of d given the sentence
x is at a maximum, where P(dx) is defined as P(d, x)/P(x).
However, there is reason to believe that no SCFG provides an acceptable
approximation of P(dx) for English. The basic problem is that SCFG's with
reasonable coverage of English typically assign significant probability to many
parses for each sentence. As a result, even if an SCFG G is successful in the
sense that the mostlikely parse according to G is almost always the correct
parse, the mostlikely parse will nonetheless have a probability significantly less
than one. In fact, it is probably a safe bet that, for SCFG's for English, the
average probability for the mostlikely parse is a good deal less than 1/2.
