Modeling hierarchical relationships in epidemiological studies: a Bayesian networks approach

Hierarchical relationships between risk factors are seldom taken into account in epidemiological studies though some authors stressed the importance of doing so, and proposed a conceptual framework in which each level of the hierarchy is modeled separately. The objective of this paper was to implement a simple version of their framework, and to propose an alternative procedure based on a Bayesian Network (BN). These approaches were illustrated in modeling the risk of diarrhea infection for 2740 children aged 0 to 59 months in Cameroon. The authors implemented a (naïve) logistic regression, a step-level logistic regression and also a BN. While the first approach is inadequate, the two others approaches both account for the hierarchical structure but to different estimates and interpretations. BN implementation showed that a child in a family in the poorest group has respectively 89%, 40% and 18% probabilities of having poor sanitation, being malnourished and having diarrhea. An advantage of the latter approach is that it enables one to determine the probability that a risk factor (and/or the outcome) is in a given state, given the states of the others. Although the BN considered here is very simple, the method can deal with more complicated models.Bayesian networks; hierarchical model; diarrhea infection; disease determinants; logistic regression

Complexity reduction of influence nets using arc removal

© 2015 - IOS Press and the authors. The model building of Influence Nets, a special instance of Bayesian belief networks, is a time-consuming and labor-intensive task. No formal process exists that decision makers/system analyst, who are typically not familiar with the underlying theory and assumptions of belief networks, can use to build concise and easy-to-interpret models. In many cases, the developed model is extremely dense, that is, it has a very high link-to-node ratio. The complexity of a network makes the already intractable task of belief updating more difficult. The problem is further intensified in dynamic domains where the structure of the built model is repeated for multiple time-slices. It is, therefore, desirable to do a post-processing of the developed models and to remove arcs having a negligible influence on the variable(s) of interests. The paper applies sensitivity of arc analysis to identify arcs that can be removed from an Influence Net without having a significant impact on its inferencing capability. A metric is suggested to gauge changes in the joint distribution of variables before and after the arc removal process. The results are benchmarked against the KL divergence metric. An empirical study based on several real Influence Nets is conducted to test the performance of the sensitivity of arc analysis in reducing the model complexity of an Influence Net without causing a significant change in its joint probability distribution

Modeling hierarchical relationships in epidemiological studies: a Bayesian networks approach

Hierarchical relationships between risk factors are seldom taken into account in epidemiological studies though some authors stressed the importance of doing so, and proposed a conceptual framework in which each level of the hierarchy is modeled separately. The objective of this paper was to implement a simple version of their framework, and to propose an alternative procedure based on a Bayesian Network (BN). These approaches were illustrated in modeling the risk of diarrhea infection for 2740 children aged 0 to 59 months in Cameroon. The authors implemented a (naïve) logistic regression, a step-level logistic regression and also a BN. While the first approach is inadequate, the two others approaches both account for the hierarchical structure but to different estimates and interpretations. BN implementation showed that a child in a family in the poorest group has respectively 89%, 40% and 18% probabilities of having poor sanitation, being malnourished and having diarrhea. An advantage of the latter approach is that it enables one to determine the probability that a risk factor (and/or the outcome) is in a given state, given the states of the others. Although the BN considered here is very simple, the method can deal with more complicated models

Modeling hierarchical relationships in epidemiological studies: a Bayesian networks approach

Hierarchical relationships between risk factors are seldom taken into account in epidemiological studies though some authors stressed the importance of doing so, and proposed a conceptual framework in which each level of the hierarchy is modeled separately. The objective of this paper was to implement a simple version of their framework, and to propose an alternative procedure based on a Bayesian Network (BN). These approaches were illustrated in modeling the risk of diarrhea infection for 2740 children aged 0 to 59 months in Cameroon. The authors implemented a (naïve) logistic regression, a step-level logistic regression and also a BN. While the first approach is inadequate, the two others approaches both account for the hierarchical structure but to different estimates and interpretations. BN implementation showed that a child in a family in the poorest group has respectively 89%, 40% and 18% probabilities of having poor sanitation, being malnourished and having diarrhea. An advantage of the latter approach is that it enables one to determine the probability that a risk factor (and/or the outcome) is in a given state, given the states of the others. Although the BN considered here is very simple, the method can deal with more complicated models

A Review of Inference Algorithms for Hybrid Bayesian Networks

Hybrid Bayesian networks have received an increasing attention during the last years. The difference with respect to standard Bayesian networks is that they can host discrete and continuous variables simultaneously, which extends the applicability of the Bayesian network framework in general. However, this extra feature also comes at a cost: inference in these types of models is computationally more challenging and the underlying models and updating procedures may not even support closed-form solutions. In this paper we provide an overview of the main trends and principled approaches for performing inference in hybrid Bayesian networks. The methods covered in the paper are organized and discussed according to their methodological basis. We consider how the methods have been extended and adapted to also include (hybrid) dynamic Bayesian networks, and we end with an overview of established software systems supporting inference in these types of models

THEORETICAL AND PRACTICAL ASPECTS OF DECISION SUPPORT SYSTEMS BASED ON THE PRINCIPLES OF QUERY-BASED DIAGNOSTICS

Diagnosis has been traditionally one of the most successful applications of Bayesian networks. The main bottleneck in applying Bayesian networks to diagnostic problems seems to be model building, which is typically a complex and time consuming task. Query-based diagnostics offers passive, incremental construction of diagnostic models that rest on the interaction between a diagnostician and a computer-based diagnostic system. Every case, passively observed by the system, adds information and, in the long run, leads to construction of a usable model. This approach minimizes knowledge engineering in model building. This dissertation focuses on theoretical and practical aspects of building systems based on the idea of query-based diagnostics. Its main contributions are an investigation of the optimal approach to learning parameters of Bayesian networks from continuous data streams, dealing with structural complexity in building Bayesian networks through removal of the weakest arcs, and a practical evaluation of the idea of query-based diagnostics. One of the main problems of query-based diagnostic systems is dealing with complexity. As data comes in, the models constructed may become too large and too densely connected. I address this problem in two ways. First, I present an empirical comparison of Bayesian network parameter learning algorithms. This study provides the optimal solutions for the system when dealing with continuous data streams. Second, I conduct a series of experiments testing control of the growth of a model by means of removing its weakest arcs. The results show that removing up to 20 percent of the weakest arcs in a network has minimal effect on its classification accuracy, and reduces the amount of memory taken by the clique tree and by this the amount of computation needed to perform inference. An empirical evaluation of query-based diagnostic systems shows that the diagnostic accuracy reaches reasonable levels after merely tens of cases and continues to increase with the number of cases, comparing favorably to state of the art approaches based on learning

Conservative Sparsification for Efficient Approximate Estimation

Linear Gaussian systems often exhibit sparse structures. For systems which grow as a function of time, marginalisation of past states will eventually introduce extra non-zero elements into the information matrix of the Gaussian distribution. These extra non-zeros can lead to dense problems as these systems progress through time. This thesis proposes a method that can delete elements of the information matrix while maintaining guarantees about the conservativeness of the resulting estimate with a computational complexity that is a function of the connectivity of the graph rather than the problem dimension. This sparsification can be performed iteratively and minimises the Kullback Leibler Divergence (KLD) between the original and approximate distributions. This new technique is called Conservative Sparsification (CS). For large sparse graphs employing a Junction Tree (JT) for estimation, efficiency is related to the size of the largest clique. Conservative Sparsification can be applied to clique splitting in JTs, enabling approximate and efficient estimation in JTs with the same conservative guarantees as CS for information matrices. In distributed estimation scenarios which use JTs, CS can be performed in parallel and asynchronously on JT cliques. This approach usually results in a larger KLD compared with the optimal CS approach, but an upper bound on this increased divergence can be calculated with information locally available to each clique. This work has applications in large scale distributed linear estimation problems where the size of the problem or communication overheads make optimal linear estimation difficult