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

This study was jointly supported by the Spanish Ministry of Education and Science under projects PID2019-106758GB-C31 and TIN2016-77902-C3-2-P, and the European Regional Development Fund (FEDER). Funding for open access charge from Universidad de Granada/CBUA.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.Spanish Government PID2019-106758GB-C31 TIN2016-77902-C3-2-PEuropean Commissio

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

The computerization of many everyday tasks generates vast amounts of data, and this has lead to the development of machine-learning methods which are capable of extracting useful information from the data so that the data can be used in future decision-making processes. For a long time now, a number of fields, such as medicine (and all healthcare-related areas) and education, have been particularly interested in obtaining relevant information from this stored data. This interest has resulted in the need to deal with increasingly complex problems which involve many different variables with a high degree of interdependency. This produces models (and in our case probabilistic graphical models) that are difficult to handle and that require very efficient techniques to store and use the information that quantifies the relationships between the problem variables. It has therefore been necessary to develop efficient structures, such as probability trees or value-based potentials, to represent the information. Even so, there are problems that must be treated using approximation since this is the only way that results can be obtained, despite the corresponding loss of information. The aim of this article is to show how the approximation can be performed with value-based potentials. Our experimental work is based on checking the behavior of this approximation technique on several Bayesian networks related to medical problems, and our experiments show that in some cases there are notable savings in memory space with limited information loss.Spanish Government PID2019-106758GB-C31European CommissionUniversidad de Granada/CBU