Using Binary Trees for the Evaluation of Influence Diagrams

Cabañas, Rafael; Gómez-Olmedo, Manuel; Cano, Andrés

doi:10.1142/s0218488516500045

Cited by 4 publications

(7 citation statements)

References 13 publications

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“…With this operation, any algorithm involving the use of approximate potentials will become approximate as well, and will ultimately offer nonexact solutions. This is helpful, since for very complex problems it is always better to have at least one approximate solution (see References [23][24][25][26] as examples of approximation with PTs).…”

Section: Discussionmentioning

confidence: 99%

“…The importance of this problem is evidenced by previous attempts to obtain alternative structures to 1DAs. Two examples of alternative approaches are standard and binary probability trees (PTs and BPTs) 20–26 . These structures can capture context‐specific independencies 20 and save memory space when repeated values appear under certain circumstances.…”

Section: Introductionmentioning

confidence: 99%

“…Two examples of alternative approaches are standard and binary probability trees (PTs and BPTs). [20][21][22][23][24][25][26] These structures can capture context-specific independencies 20 and save memory space when repeated values appear under certain circumstances. These representations also allow to obtain approximations through pruning operations: Assuming a loss of information, some contiguous values can be substituted by their average value to reduce memory space.…”

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confidence: 99%

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

Gómez-Olmedo

Cabañas

Cano

et al. 2021

Int J of Intelligent Sys

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Gómez-Olmedo

Cabañas

Cano

et al. 2021

Int J of Intelligent Sys

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“…Jensen and Dittmer (1994) developed an efficient algorithm to compute IDs, using BNs, which uses a strong JT with a special propagation scheme to calculate expected utilities. Cabanas et al (2016) exploited context-specific independencies for inference by encoding the parameters of IDs in tree structures. Lazy propagation (Cabanas et al, 2013, Madsen and Jensen, 1999, Madsen and Nilsson, 2001) and sampling based approximate algorithms (Cano et al, 2006) have also been used to compute large IDs efficiently.…”

Section: Influence Diagrams (Ids)mentioning

confidence: 99%

An improved method for solving Hybrid Influence Diagrams

Yet

Neil

Fenton

et al. 2018

International Journal of Approximate Reasoning

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While decision trees are a popular formal and quantitative method for determining an optimal decision from a finite set of choices, for all but very simple problems they are computationally intractable. For this reason, Influence Diagrams (IDs) have been used as a more compact and efficient alternative. However, most algorithmic solutions assume that all chance variables are discrete, whereas in practice many are continuous. For such 'Hybrid' IDs (HIDs) the current-stateof-the-art algorithms suffer from various limitations on the kinds of inference that can be performed. This paper presents a novel method that overcomes a number of these limitations. The method solves a HID by transforming it to a Hybrid Bayesian Network (HBN) and carrying out inference on this HBN using Dynamic Discretization (DD). It generates a simplified decision tree from the propagated HBN to compute and present the optimal decisions under different decision scenarios. To provide satisfactory performance the method uses 'inconsistent evidence' to model functional and structural asymmetry. By using the entire marginal probability distribution of the continuous utility and chance nodes, rather than expected values alone, our method also enhances decision analysis by offering the possibility to consider additional statistics other than expected utility, such as measures of risk. We illustrate our method by using the oil wildcatter example and 2 its variations with continuous nodes. We also use a financial score to combine risk and return measures, for illustration.

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“…And another approaches have been explored over the years in the search for efficient alternative representations to 1DAs, which are able to work with complex models. Successful examples are standard and binary probability trees (PTs and BPTs) [9][10][11][12][13]. Despite the advantages that these offer compared to the use of 1DA, they also present certain limitations, and not all context-specific independences can result in smaller representations and therefore in memory space savings.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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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.

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Using Binary Trees for the Evaluation of Influence Diagrams

Cited by 4 publications

References 13 publications

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

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

An improved method for solving Hybrid Influence Diagrams

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

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