  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 multiple modules to
create more accurate solutions. This paper examines three merging rules for
combining probability distributions: the familiar mixture rule, the logarithmic
rule, and a novel product rule. These rules were applied with state-of-the-art
results to two problems 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.
