Nonuniform Dynamic Discretization in Hybrid Networks

TL;DR

This paper introduces a nonuniform discretization method for hybrid networks that reduces data structure size and improves inference accuracy, using a new BSP tree data structure and an iterative algorithm that refines discretization with evidence.

Contribution

It presents a novel nonuniform discretization approach with BSP trees and an iterative algorithm for improved probabilistic inference in hybrid networks.

Findings

BSP trees can be exponentially smaller than uniform discretization structures.

Nonuniform discretization reduces information loss and improves inference accuracy.

The iterative algorithm converges and enhances results with evidence.

Abstract

We consider probabilistic inference in general hybrid networks, which include continuous and discrete variables in an arbitrary topology. We reexamine the question of variable discretization in a hybrid network aiming at minimizing the information loss induced by the discretization. We show that a nonuniform partition across all variables as opposed to uniform partition of each variable separately reduces the size of the data structures needed to represent a continuous function. We also provide a simple but efficient procedure for nonuniform partition. To represent a nonuniform discretization in the computer memory, we introduce a new data structure, which we call a Binary Split Partition (BSP) tree. We show that BSP trees can be an exponential factor smaller than the data structures in the standard uniform discretization in multiple dimensions and show how the BSP trees can be used in the standard join tree algorithm. We show that the accuracy of the inference process can be significantly improved by adjusting discretization with evidence. We construct an iterative anytime algorithm that gradually improves the quality of the discretization and the accuracy of the answer on a query. We provide empirical evidence that the algorithm converges.