Inference in Polytrees with Sets of Probabilities

TL;DR

This paper introduces new algorithms for inference in polytrees with probability sets and intervals, significantly improving computational efficiency and providing both approximate and exact solutions.

Contribution

It presents a substantial improvement on existing algorithms and introduces a new local search method for inference in polytrees with probability intervals.

Findings

Dramatic reduction in computational effort for inference tasks

New algorithms outperform existing methods in efficiency

Branch-and-bound methods can produce exact or approximate solutions

Abstract

Inferences in directed acyclic graphs associated with probability sets and probability intervals are NP-hard, even for polytrees. In this paper we focus on such inferences, and propose: 1) a substantial improvement on Tessems A / R algorithm FOR polytrees WITH probability intervals; 2) a new algorithm FOR direction - based local search(IN sets OF probability) that improves ON existing methods; 3) a collection OF branch - AND - bound algorithms that combine the previous techniques.The first two techniques lead TO approximate solutions, WHILE branch - AND - bound procedures can produce either exact OR approximate solutions.We report ON dramatic improvements ON existing techniques FOR inference WITH probability sets AND intervals, IN SOME cases reducing the computational effort BY many orders OF magnitude.