The computation of first order moments on junction trees

TL;DR

This paper reviews methods for computing first order moments on junction trees, focusing on algorithms that optimize memory usage by leveraging the structure of junction trees.

Contribution

It compares existing algorithms for first order moments computation, highlighting their memory efficiency based on junction tree properties.

Findings

Lauritzen-Nilsson algorithm uses leaf-set memory space.

Mauá et al. algorithm employs leaf-set memory for normalization.

Vertices problem approach reduces memory to edge-set size.

Abstract

We review some existing methods for the computation of first order moments on junction trees using Shafer-Shenoy algorithm. First, we consider the problem of first order moments computation as vertices problem in junction trees. In this way, the problem is solved using the memory space of an order of the junction tree edge-set cardinality. After that, we consider two algorithms, Lauritzen-Nilsson algorithm, and Mau\'a et al. algorithm, which computes the first order moments as the normalization problem in junction tree, using the memory space of an order of the junction tree leaf-set cardinality.