Likelihood Computations Using Value Abstractions

TL;DR

This paper introduces evidence-specific value abstraction techniques to accelerate Bayesian network inference by grouping variable values, reducing computational costs, especially in complex networks with many hidden variables, and demonstrates its effectiveness on genetic linkage problems.

Contribution

The paper formalizes safe value abstraction for Bayesian inference and develops algorithms that leverage these abstractions to speed up likelihood computations in learning tasks.

Findings

Value abstraction exploits regularities in probability distributions.

Significant speedups in likelihood computations for complex networks.

Effective application demonstrated on genetic linkage problems.

Abstract

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.