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Use of Linear Weights in BBN Modelling

IP.com Disclosure Number: IPCOM000012495D
Original Publication Date: 2003-May-12
Included in the Prior Art Database: 2003-May-12

Publishing Venue

Motorola

Related People

Jean-Jacques Gras: AUTHOR [+3]

Abstract

Bayesian Belief Network models (BBNs or BNs) can be constructed directly from data, but also through elicitation sessions with domain experts. The process involves painstaking discussions with the experts to quantify the probabilistic relationships (conditional probability) for each Node Probability Table (NPT). This can be intractable for nodes with a high number of states, especially continuous nodes. We propose the use of linear weights in BBN modelling as, often, the relation between continuous factors can be approximated by a linear function. The elicitation and construction of the node probability table is then fast and simple.

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Authors: Jean-Jacques Gras, David McGaw, Qiang Fu

Abstract:

Bayesian Belief Network models (BBNs or BNs) can be constructed directly from data, but also through elicitation sessions with domain experts. The process involves painstaking discussions with the experts to quantify the probabilistic relationships (conditional probability) for each Node Probability Table (NPT). This can be intractable for nodes with a high number of states, especially continuous nodes. We propose the use of linear weights in BBN modelling as, often, the relation between continuous factors can be approximated by a linear function.� The elicitation and construction of the node probability table is then fast and simple.

1.    Introduction

Systems that are subject to uncertainty in their behaviour can be modelled by Bayesian Belief Networks (BBNs). The applications are numerous and the number of companies investing in this new technology is rapidly growing since, in recent years, efficient algorithms and tools have been made available.

BBNs are a graphical representation of probabilistic relationships. With BBNs it is easy to represent these relationships between the uncertain variables or factors that are contributing to the state of the system. In these models, a graph expresses explicitly the qualitative relationships of conditional dependence and independence between variables. The quantitative specifications of the relations between variables involve probability distributions, which are embedded within node probability tables (NPTs) residing in each node.

When a system is perfectly understood so that all contributing factors have been identified along with a large sample of available data, BBNs can be constructed directly from that data, like in data mining applications. However, most of their benefit is achieved when there is a need to analyse a system while modelling it. This is done through elicitation sessions with experts in the domain being modelled. Each fragment of the graph, formed by a node and its direct parents, is analysed to build its NPT. Progressively the whole model is integrated.

Usually, a consensus on the factors and their relations in the model is relatively easily reached. The quantification of these relations for each fragment is, in practice, only done on a limited number of combinations of parents’ values, because domain experts are generally incapable of providing complete (conditional) probabilities. But the process still involves painstaking discussions to evaluate the child distribution for each of the several (5 usually) typical scenarios. The model designer then does an even more painstaking analysis of these (5) distributions to find a general equation that is applicable to all possible scenarios. This equation is used to interpolate between the elicited scenarios and generate the child distribution for each possible set of parent values.

This process takes about...