On Selecting the Optimal Bayesian Network Model Construction Approach (original) (raw)
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Bayesian Networks, 2012
Bayesian networks (BNs) is probabilistic graphical models that are widely used for building expert systems in several application domains. In the context of expert systems, either probabilistic or heuristic, the development of explanation facilities is important for three main reasons. First, the construction of those systems with the help of human experts is a difficult and time consuming task, and prone to errors and omissions. A Bayesian network tool can help the knowledge engineers and experts who are taking part in the project to debug the system when it does not yield the expected results and even before a malfunction occurs. Second, human beings are reluctant to accept the advice that is offered by a machine if they are not able to understand how the system arrived at those recommendations. Third, an expert system that is used as an intelligent tutor must be able to communicate to the apprentice the knowledge it contains, the way in which the knowledge has been applied to arrive at a conclusion, and what would have happened if the user had introduced different pieces of evidence (what-if reasoning). One of the most difficult obstacles in the practical application of probabilistic methods is the effort that is required for model building and, in particular, for quantifying graphical models with numerical probabilities. The construction o f B a y e s i a n N e t w o r k s (B N s) w i t h t h e h e l p o f h u m a n e x p e r t s i s a d i f f i c u l t a n d t i m e consuming task, which is prone to errors and omissions especially when the problems are very complicated or there are numerous variables involved. Learning the structure of a BN model and causal relations from a dataset or database is important for extensive BNs analysis. In general, the causal structure and the numerical parameters of a BN can be obtained using two distinct approaches. First, they can be obtained from an expert. Second, they can also be learned from a data set. The main drawback of the first approach is that sometimes there is not enough causal knowledge to establish the structure of the network model with certainty and estimation of probabilities required for a typical application is a time-consuming task because of the number of parameters required (typically hundreds or even thousands of values). Thus, the second approach can initially help human experts or a group of experts build a BN model and they can make it applicable at a later time. In practice, some combination of these two approaches is typically used.
Modeling Bayesian Networks by Learning from Experts
Bnaic, 2005
Bayesian network modeling by domain experts is still mainly a process of trial and error. The structure of the graph and the specification of the conditional probability tables (CPTs) are in practice often fiddled until a desired model behavior is obtained. We describe a development tool in which graph specification and CPT modeling are fully separated. Furthermore, the tuning of CPTs is handled automatically. The development tool consists of a database in which the graph description and the desired probabilistic behavior of the network are separately stored. From this database, the graph is constructed and the CPTs are numerically optimized in order to minimize the error between desired and actual behavior. The tool may be helpful in both development and maintenance of probabilistic expert systems. A demo is provided. A numerical example illustrates the methodology.
An optimization-based approach for the design of Bayesian networks
Mathematical and Computer Modelling, 2008
Bayesian networks model conditional dependencies among the domain variables, and provide a way to deduce their interrelationships as well as a method for the classification of new instances. One of the most challenging problems in using Bayesian networks, in the absence of a domain expert who can dictate the model, is inducing the structure of the network from a large, multivariate data set. We propose a new methodology for the design of the structure of a Bayesian network based on concepts of graph theory and nonlinear integer optimization techniques.
Exploiting Experts’ Knowledge for Structure Learning of Bayesian Networks
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016
Learning Bayesian network structures from data is known to be hard, mainly because the number of candidate graphs is super-exponential in the number of variables. Furthermore, using observational data alone, the true causal graph is not discernible from other graphs that model the same set of conditional independencies. In this paper, it is investigated whether Bayesian network structure learning can be improved by exploiting the opinions of multiple domain experts regarding cause-effect relationships. In practice, experts have different individual probabilities of correctly labeling the inclusion or exclusion of edges in the structure. The accuracy of each expert is modeled by three parameters. Two new scoring functions are introduced that score each candidate graph based on the data and experts' opinions, taking into account their accuracy parameters. In the first scoring function, the experts' accuracies are estimated using an expectation-maximization-based algorithm and the estimated accuracies are explicitly used in the scoring process. The second function marginalizes out the accuracy parameters to obtain more robust scores when it is not possible to obtain a good estimate of experts' accuracies. The experimental results on simulated and real world datasets show that exploiting experts' knowledge can improve the structure learning if we take the experts' accuracies into account.
Complexity
One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions, and by the fact that the problem is NP-hard. Hence, full enumeration of all the possible solutions is not always feasible and approximations are often required. However, to the best of our knowledge, a quantitative analysis of the performance and characteristics of the different heuristics to solve this problem has never been done before. For this reason, in this work, we provide a detailed comparison of many different state-of-the-arts methods for structural learning on simulated data considering both BNs with discrete and continuous variables, and with different rates of noise in the data. In particular, we investigate the performance of different widespread scores and algorithmic approaches proposed for the inference and the statistical pitfalls within them.
2008
Bayesian Networks (BNs) model problems that involve uncertainty. A BN is a directed graph, whose nodes are the uncertain variables and whose edges are the causal or influential links between the variables. Associated with each node is a set of conditional probability functions that model the uncertain relationship between the node and its parents. The benefits of using BNs to model uncertain domains are well known, especially since the recent breakthroughs in algorithms and tools to implement them. However, there have been serious problems for practitioners trying to use BNs to solve realistic problems. This is because, although the tools make it possible to execute largescale BNs efficiently, there have been no guidelines on building BNs. Specifically, practitioners face two significant barriers. The first barrier is that of specifying the graph structure such that it is a sensible model of the types of reasoning being applied. The second barrier is that of eliciting the conditional probability values. In this paper we concentrate on this first problem. Our solution is based on the notion of generally applicable "building blocks", called idioms, which serve solution patterns. These can then in turn be combined into larger BNs, using simple combination rules and by exploiting recent ideas on modular and Object Oriented BNs (OOBNs). This approach, which has been implemented in a BN tool, can be applied in many problem domains. We use examples to illustrate how it has been applied to build large-scale BNs for predicting software safety. In the paper we review related research from the knowledge and software engineering literature to provide some context to the work and to support our argument that BN knowledge engineers require the same types of processes, methods and strategies enjoyed by systems and software engineers if they are to succeed in producing timely, quality and cost-effective BN decision support solutions.
Improving the Applicability of the Ranked Nodes Method to build Expert-Driven Bayesian Networks (S)
International Conferences on Software Engineering and Knowledge Engineering, 2019
One challenge in constructing a Bayesian network (BN) is defining the node probability tables (NPTs), which can be learned from data or elicited from domain experts. In practice, for large-scale BN it is common not to have enough data for learning and elicitation from experts is unfeasible. Previous work proposed a solution to this problem: the Ranked Nodes Method (RNM). However, this solution needs to be applied by a RNM expert who, through the elicitation of expert judgement, identifies the necessary parameters for the RNM algorithm to generate the NPTs. Hence, this paper presents a novel approach to define NPT using the RNM with no ranked nodes-specific knowledge. The solution is named Simulated Bayesian Network Expert (SBNE). It consists of eliciting a subset of the NPT from the domain experts which is used as input to an algorithm that estimates the optimal parameters for the RNM to generate the NPTs. To validate our solution, we conducted an experiment with multiple domain experts and compared the results with other methods. Our solution outperformed the other methods (producing NPTs at least 12% more accurate) and is, therefore, a promising approach to apply RNM without relying on RNM experts.
Improving the Applicability of Bayesian Networks through Production Rules
Proceedings of the 28th International Conference on Software Engineering and Knowledge Engineering, 2016
One of the key challenges in constructing a Bayesian network BN is defining the node probability tables (NPT). For large-scale BN, learning NPT through domain experts knowledge elicitation is unfeasible. Previous works proposed solutions to this problem using the concept of ranked nodes; however, they have limited modeling capabilities or rely on BN experts to apply them, reducing their applicability. In this paper, we present an expert system based on production rules to define NPTs with the purpose of enabling the definition of NPTs by experts with no ranked nodes-specific knowledge. To create the rules, we elicited data from an expert in ranked nodes. To validate our approach, we executed an experiment with a BN already published in the literature to verify if, with our approach, a practitioner can achieve the same or better configuration for the NPTs. We used the Brier score to assess the NPTs accuracy and evaluated the results with the Wilcoxon test. All the Wilcoxon tests executed rejected the null hypotheses that stated that the Brier scores for the original NPTs method were the same as the new NPTs. By using our solution, a practitioner can accurately define NPTs without understanding the concept of ranked nodes.
Building Large-Scale Bayesian Networks
Knowledge Engineering Review, 1999
Bayesian Networks (BNs) model problems that involve uncertainty. A BN is a directed graph, whose nodes are the uncertain variables and whose edges are the causal or influential links between the variables. Associated with each node is a set of conditional probability functions that model the uncertain relationship between the node and its parents. The benefits of using BNs to