Likelihood Computations Using Value Abstractions
  In this paper, we use evidence-specific value abstraction for speeding
Bayesian networks inference. This is done by grouping variable values and
treating the combined values as a single entity. As we show, such abstractions
can exploit regularities in conditional probability distributions and also the
specific values of observed variables. To formally justify value abstraction,
we define the notion of safe value abstraction and devise inference algorithms
that use it to reduce the cost of inference. Our procedure is particularly
useful for learning complex networks with many hidden variables. In such cases,
repeated likelihood computations are required for EM or other parameter
optimization techniques. Since these computations are repeated with respect to
the same evidence set, our methods can provide significant speedup to the
learning procedure. We demonstrate the algorithm on genetic linkage problems
where the use of value abstraction sometimes differentiates between a feasible
and non-feasible solution.
