Context-Specific Approximation in Probabilistic Inference

TL;DR

This paper introduces a context-specific approximation method for probabilistic inference that simplifies models by ignoring similar distinctions, providing bounds on errors and preliminary empirical results.

Contribution

It proposes a structured approach to simplify Bayesian networks by ignoring negligible distinctions in certain contexts, enhancing inference efficiency.

Findings

Simplifies probabilistic models by ignoring similar probabilities.

Provides bounds on approximation errors.

Preliminary empirical results on simple networks show promise.

Abstract

There is evidence that the numbers in probabilistic inference don't really matter. This paper considers the idea that we can make a probabilistic model simpler by making fewer distinctions. Unfortunately, the level of a Bayesian network seems too coarse; it is unlikely that a parent will make little difference for all values of the other parents. In this paper we consider an approximation scheme where distinctions can be ignored in some contexts, but not in other contexts. We elaborate on a notion of a parent context that allows a structured context-specific decomposition of a probability distribution and the associated probabilistic inference scheme called probabilistic partial evaluation (Poole 1997). This paper shows a way to simplify a probabilistic model by ignoring distinctions which have similar probabilities, a method to exploit the simpler model, a bound on the resulting errors, and some preliminary empirical results on simple networks.