Value‐based potentials: Exploiting quantitative information regularity patterns in probabilistic graphical models

Abstract

When dealing with complex models (i.e., models with many variables, a high degree of dependency between variables, or many states per variable), the efficient representation of quantitative information in probabilistic graphical models (PGMs) is a challenging task. To address this problem, this study introduces several new structures, aptly named value‐based potentials (VBPs), which are based exclusively on the values. VBPs leverage repeated values to reduce memory requirements. In the present paper, they are compared with some common structures, like standard tables or unidimensional arrays, and probability trees (PT). Like VBPs, PTs are designed to reduce the memory space, but this is achieved only if value repetitions correspond to context‐specific independence patterns (i.e., repeated values are related to consecutive indices or configurations). VBPs are devised to overcome this limitation. The goal of this study is to analyze the properties of VBPs. We provide a theoretical analysis of VBPs and use them to encode the quantitative information of a set of well‐known Bayesian networks, measuring the access time to their content and the computational time required to perform some inference tasks.

Using Value-Based Potentials for Making Approximate Inference on Probabilistic Graphical Models

“…Valued-based potentials were recently introduced [16] as an alternative representation based exclusively on the values. Once such new structure was applied on several BNs from two different sources (bnlearn repository [17,18] and UAI competitions [19,20]) and compared with 1DAs, PTs, and PPTs.…”

“…VBP structures [16] may produce a relevant decrease in the memory space when repeated values are present. Moreover, the approximation operation can be applied in a very simple way.…”

“…Value-based potentials (VBPs) [16] were recently introduced. These structures take advantage of the repetition of values, regardless of the order in which they appear.…”

“…As VBPs represent potentials, it will be easy to adapt inference algorithms to use VBPs. A more complete definition of VBPs can be found in [16].…”

“…The purpose of VBPs is therefore to make as many groups as different probability values exist to avoid repetitions and associate the related indices of configurations. From the alternatives presented in [16], in this paper we will focus on value-driven with indices (VDI) and index-driven with pairs (IDP), since both of these performed extremely well on most of the studied BNs.…”