انتزاعات سازگار و ناسازگار در شبکه های بیزی

The graphical structure of a Bayesian network (BN) makes it a technology well-suited for developing decision support models from a combination of domain knowledge and data. The domain knowledge of experts is used to determine the graphical structure of the BN, corresponding to the relationships and between variables, and data is used for learning the strength of these relationships. However, the available data seldom match the variables in the structure that is elicited from experts, whose models may be quite detailed; consequently, the structure needs to be abstracted to match the data. Up to now, this abstraction has been informal, loosening the link between the final model and the experts’ knowledge. In this paper, we propose a method for abstracting the BN structure by using four ‘abstraction’ operations: node removal, node merging, state-space collapsing and edge removal. Some of these steps introduce approximations, which can be identified from changes in the set of conditional independence (CI) assertions of a network.

A knowledge-based Bayesian network (BN) aims to model the data-generating process of a problem domain by encoding knowledge about influences and independences between the important variables of the domain. The first step in building the BN is for a knowledge engineer to elicit the structure of the BN from domain experts. When the structure is finalised, any available data can be used to learn the parameters of the BN or, if no data are available, the parameters can also be elicited. This paper is about the knowledge engineering techniques used in the first stage of this process: the development of the BN structure. Knowledge-engineered BNs are often developed through multiple stages as the knowledge engineers and the domain experts refine the model iteratively [8]. The initial knowledge model is often large and detailed, and some elements of the model may need to be simplified or abstracted as data is lacking or the parameters are too difficult to elicit. However, even simple abstraction operations, such as removing a node, can result in numerous and complicated alternative BNs which are difficult for the knowledge engineers to evaluate without a structured method. The effects of these abstractions must be carefully examined by domain experts to prevent any unwanted changes in the modelled knowledge of the data generating process. Moreover, the way that the final BN has been derived needs to be presented thoroughly so that the knowledge base of the model and its derivation is understandable. Our aim is to present a method of abstracting a BN structure. The method is developed for knowledge engineers developing a BN structure with domain experts. The method provides a set of abstraction operations which together: 1. Allow a BN to be simplified by removing and merging nodes, removing edges and reducing the number of states. 2. Distinguish abstractions that add to the knowledge base from those compatible with the knowledge elicited so far, so that the added knowledge can be confirmed by domain experts. 3. Provide a way to show the link between the initial and abstracted models, in the form of a derivation that captures the complete sequence of abstraction operations. The method can be used to help knowledge engineers to select the most suitable model refinements by evaluating alternative abstractions, in consultation with domain experts. The selection may also be guided by considering the availability of data or compatibility with causal relationships. Our knowledge engineering method is based on well-known techniques mainly used for learning and inference problems [17], [22], [21] and [3]. Our main contribution is to explore knowledge engineering aspect of these operations. The remainder of this paper is organised as follows: Section 2 reviews the related work. Section 3 gives an overview of the relation between knowledge and conditional independences (CI) in BNs. Section 4 introduces abstraction as a knowledge engineering method and Section 5 describes the abstraction operations of this method and examines their compatibility properties. These operations are illustrated by a medical case-study in Section 6. Section 7 shows the graphical representation of the abstraction operations, and Section 8 presents the conclusions.

This paper proposed abstraction as a knowledge engineering method for simplifying the structure of a BN. The method is illustrated by a medical case study about haemorrhagic shock. Our method provided: 1. A sufficient set of operations that simplify a BN by removing and merging nodes, removing edges and reducing the number of states. 2. The compatibility properties of each abstraction in terms of CIs added to the BN structure. 3. A graphical notation that captures the sequence and type of abstraction operations, and thereby showing the link between the knowledge-base and the abstracted BN. Some of the abstraction operations in our method are based on existing techniques that have been mainly used for learning and inference problems. This paper emphasises the potential of these techniques for following a systematic approach to knowledge engineering. The compatible abstraction operations do not add CIs but they can make the BN structure increasingly complex by adding edges. Incompatible abstraction can be used to simplify the structure but they approximate the BN structure by adding new CI conditions. Trade-offs between the approximations and complexity must be considered carefully since some approximations can significantly change the underlying domain knowledge while simplifying the BN. Our abstraction methodology allows domain experts and knowledge engineers to evaluate these trade-offs by explicitly showing the changes in the underlying domain knowledge. 8.1. Comparison with existing abstraction techniques The main motivation from ABEL was its ability of reasoning in multiple levels of abstraction by showing the link between different levels (see Section 2.1). Our abstraction methodology can show the link between the underlying knowledge and simplifications in a similar way to ABEL. However, ABEL’s abstractions are dynamically made at the inference stage based on its medical knowledge database, strongly guided by available data. ABEL uses its abstraction mechanism to create causal models that explain the observed state of a patient. BNs are more sophisticated than the causal diagrams in ABEL as they are composed of variables with multiple states. A single BN can be instantiated in different ways according to observed values rather than creating different models for different observations. Therefore, our aim is to build a BN model that represents the best available knowledge and evidence, and our abstraction methodology is applied statically by knowledge engineers and domain experts at the development stage of the model. The aim of our abstraction methodology is not aligned with idioms, network fragments, OOBNs, parent divorcing approach and similarity networks (see Section 2.2). These techniques aim to assist BN development and maintenance either by using semantically meaningful BN fragments or merging BN fragments or introducing nodes. However, the aim of our abstraction technique is to allow BN simplification without losing the link to domain knowledge supporting the BN. The aims of Wu and Poh’s abstraction operations [23] and Srinivas’s hierarchical approach [20] are similar to our abstraction methodology. However, Wu and Poh’s operations can only be applied to limited and simple modelling tasks. The merged variables, for instance, must share only a single parent or child. The abstraction operations in this paper overcome these limitations as they can be applied to any node, edge or state in a BN. Srinivas uses node removal technique to model different levels of abstraction for a specific engineering problem. Our abstraction methodology is not developed for a specific problem, and contains a wider variety of abstraction techniques. We presented general properties of the abstraction techniques for BNs and use a medical case study only to illustrate the application of these techniques. In summary, our abstraction methodology overcomes the limitations of these studies as it is not developed for a specific problem, and its operations can be applied to any element of a BN. 8.2. Future work The case-study illustrates the application of the abstraction methodology to a real-world problem. Further case studies could focus on evaluating the practical impact of the abstraction methodology on BN development. The evaluation could be composed of two steps. The first step could assess the degree of knowledge that becomes unclear to users when BN models are simplified without using the abstraction methodology. The second step could evaluate the impact of the abstraction methodology to improve understanding of the BN. The next stage in this research is to implement the abstraction operations in BN software such as AgenaRisk [1]. The BN software, supplemented with the abstraction operations, would guide knowledge engineers and support BN development by showing the impacts of compatible abstractions and presenting the approximations resulting from incompatible abstractions. The abstraction operations could also be coupled with an evidence framework that shows evidence supporting every node, edge and state in a BN. As a result, the evidence framework could show how abstraction operations affect the underlying evidence. This would assist knowledge engineers by showing evidence that supports or contradicts with a particular abstraction operation.