  Existing statistical approaches to natural language problems are very coarse
approximations to the true complexity of language processing. As such, no
single technique will be best for all problem instances. Many researchers are
examining ensemble methods that combine the output of successful, separately
developed modules to create more accurate solutions. This paper examines three
merging rules for combining probability distributions: the well known mixture
rule, the logarithmic rule, and a novel product rule. These rules were applied
with state-of-the-art results to two problems commonly used to assess human
mastery of lexical semantics -- synonym questions and analogy questions. All
three merging rules result in ensembles that are more accurate than any of
their component modules. The differences among the three rules are not
statistically significant, but it is suggestive that the popular mixture rule
is not the best rule for either of the two problems.
