BAYESIAN NETWORK WITH INTERVAL PROBABILITY PARAMETERS

General Bayesian Network Approach to Health Informatics Prediction: Emphasis on Performance Comparison

We propose a Bayesian higher-order probability logic reasoning approach with interval probability parameters to the problem of making inference from conditional knowledge, which combines weak conditional probability and conditional event algebra for approximate inferences. We define the bound-limited weak conditional interval probabilities, the corresponding probabilistic description, and the multiplication rules of weak conditional probabilities for joint probability distribution, and use higher-order conditional event to resolve a discrepancy between logic and probability. By extending normal measurable space with conditional event, we bring logic consistent with probability in denoting conditional knowledge, and then transform a higher-order conditional event to normal events and corresponding logical joint events via conditional event algebra. Based on multiplication rules, we compute the quantitative values of the events with interval parameters, and evaluate the value of higher-order conditional event and finish reasoning process. An illustrative example of application of our method shows how we make inferences from conditional knowledge.

This paper proposes the general Bayesian network as a tool for identifying critical dependencies among complex human beliefs, especially for the case of airline service industry. When we consider an overall efficacy of the flight operation, to understand underlying beliefs between pilots and controllers is critical. However, even for the experts in organizational behavior, it is difficult to identify dependencies among such the beliefs. To tackle this ambiguous issue, we suggest the use of the general Bayesian network to automatically generate interesting hypotheses. The experimental results reveal the possibility of selective attention to the critical dependencies for achieving enhanced efficacy.

2U: an exact interval propagation algorithm for polytrees with binary variables

It is widely conjectured that the excellent ROC performance of biological vision systems is due in large part to the exploitation of context at each of many levels in a part/whole hierarchy. We propose a mathematical framework (a machine) for constructing probabilistic hierarchical image models, designed to accommodate arbitrary contextual relationships, and we build a demonstration system for reading Massachusetts license plates in an image set collected at Logan Airport. The demonstration system detects and correctly reads more than 98% of the plates, with a negligible rate of false detection. Unlike a formal grammar, the architecture of a composition machine does not exclude the sharing of sub-parts among multiple entities, and does not limit interpretations to single trees (e.g. a scene can have multiple license plates, or no plates at all). In this sense, the architecture is more like a general Bayesian network than a formal grammar. On the other hand, unlike a Bayesian network, the distribution is non-Markovian, and therefore more like a probabilistic context-sensitive grammar. The conceptualization and construction of a composition machine is facilitated by its formulation as the result of a series of non-Markovian perturbations of a Markov backbone.

Bayesian networks are often proposed as a method for high-level information fusion. However, a Bayesian network relies on strong assumptions about the underlying probabilities. In many cases it is not realistic to require such precise probability assessments. We show that there exists a significant set of problems where credal networks outperform Bayesian networks, thus enabling more dependable decision making for this type of problems. A credal network is a graphical probabilistic method that utilizes sets of probability distributions, e.g., interval probabilities, for representation of belief. Such a representation allows one to properly express epistemic uncertainty, i.e., uncertainty that can be reduced if more information becomes available. Since reducing uncertainty has been proposed as one of the main goals of information fusion, the ability to represent epistemic uncertainty becomes an important aspect in all fusion applications.

The analysis of high-dimensional microbiome multiomics datasets is crucial for understanding the complex interactions between microbial communities and host physiological states across health and disease conditions. Despite their importance, current methods, such as the microbe-metabolite vectors approach, often face challenges in predicting metabolite abundances from microbial data and identifying keystone species. This arises from the vast dimensionality of metagenomics data, which complicates the inference of significant relationships, particularly the estimation of co-occurrence probabilities between microbes and metabolites. Here we propose the variational Bayesian microbiome multiomics (VBayesMM) approach, which aims to improve the prediction of metabolite abundances from microbial metagenomics data by incorporating a spike-and-slab prior within a Bayesian neural network. This allows VBayesMM to rapidly and precisely identify crucial microbial species, leading to more accurate estimations of co-occurrence probabilities between microbes and metabolites, while also robustly managing the uncertainty inherent in high-dimensional data. Moreover, we have implemented variational inference to address computational bottlenecks, enabling scalable analysis across extensive multiomics datasets. Our large-scale comparative evaluations demonstrate that VBayesMM not only outperforms existing methods in predicting metabolite abundances but also provides a scalable solution for analyzing massive datasets. VBayesMM enhances the interpretability of the Bayesian neural network by identifying a core set of influential microbial species, thus facilitating a deeper understanding of their probabilistic relationships with the host.

There is complex uncertainty involved in evaluation of equipment sensitivity to voltage sags, and that makes it difficult for the point-valued assessment method to evaluate the impact of voltage sags on the sensitive equipment, especially in the case of small sample size. Considering the multi-valued nature of equipment status during the voltage sags, the voltage tolerance level of sensitive equipment is characterized by interval data, so as to derive interval probabilities of equipment operation status. Meanwhile, hybrid entropy is then used to measure the uncertainty of randomness and fuzziness in equipment voltage tolerance level. It develops one novel model by transforming the interval probability into point-valued probability based on maximum hybrid entropy model. By the help of personal computers, the proposed model is finally verified in a test distribution system.

The football match outcome prediction particularly has gained popularity in recent years. It attract lots type of fan from the analyst expert, managerial of football team and others to predict the football match result before the match start.There are three types of approaches had been proposed to predict win, lose or draw; and evaluate the attributes of the football team. The approaches are statistical approach, machine learningapproach and Bayesian approach. This paper propose the Bayesian approaches within machine learning approaches such as Naive Bayes (NB), Tree Augmented Naive Bayes (TAN) and General Bayesian Network (K2) to predict the football match outcome. The required of football data is the English Premier League match results for three seasons; 2016 – 2017, 2015 – 2016 and 2014 – 2015 downloaded from http://www.football-data.co.uk. The experimental results showed that TAN achieved the highest predictive accuracy of 90.0 % in average across three seasons among others Bayesian approach (K2 and NB). The result from this research is hope that it can be used in future research for predicting the football match outcome.

More Complex Cases: General Bayesian Networks

In many applications, one can define a large set of features to support the classification task at hand. At test time, however, these become prohibitively expensive to evaluate, and only a small subset of features is used, often selected for their information-theoretic value. For threshold-based, Naive Bayes classifiers, recent work has suggested selecting features that maximize the expected robustness of the classifier, that is, the expected probability it maintains its decision after seeing more features. We propose the first algorithm to compute this expected same-decision probability for general Bayesian network classifiers, based on compiling the network into a tractable circuit representation. Moreover, we develop a search algorithm for optimal feature selection that utilizes efficient incremental circuit modifications. Experiments on Naive Bayes, as well as more general networks, show the efficacy and distinct behavior of this decision-making approach.

This paper deals with the problem of coordinating a team of mobile sensor platforms searching for a single mobile non-evading target. It follows the general Bayesian active sensor network approach introduced in [2] where each decision maker plans locally based on an equivalent representation of the target state probability density function (PDF). This paper focuses on the prediction stage of the decentralized Bayesian filter. It looks at how different types of realistic external constraints may affect the target motion and how they may be taken into account in the process model. Two general classes of constraints are identified soft and hard. A few constraint examples from each class are given to illustrate their impact on the evolution of the target state PDF. Multiple constraints of various types can be combined to increase the accuracy of the predicted PDF estimate, thus affecting the individual trajectories of the search platforms. The effectiveness of the framework is demonstrated for a team of airborne search vehicles looking for a drifting target lost in a storm at sea.

This paper develops a model validation method in the case of the full scale tests for the system model are infeasible. The Bayesian network with uncertain conditional probability parameters is used to represent the relations between the large computational model and its smaller modules. The interval probability theory is adopted to extrapolate the posterior probability of the interested variable in the uncertain Bayesian network. An interval valued Bayes factor is obtained to be the metric for model validation.

During the last decades, "Transport Demand" and "Mobility" has been a continuously developing branch in the transport literature.This is reflected in the great amount of research papers published in scientific magazines dealing with trip matrix estimation (see (Doblas & Benítez, 2005)) and traffic assignment problems (see (Praskher & Bekhor, 2004)).Current traffic models reproduce the mobility using several data inputs, in particular prior trip matrix, link counts, etc. (see (Yang & Zhou, 1998)) which are data only from a subset of the problem variables, and its size will depend on the available budget for the study being carried on.Among the problems faced for solving these models we can emphasize the high number of possible solutions which is usually solved by choosing the solution where the model results best fits real data.Nevertheless a model does not have to reproduce only the real data, but also must reproduce accurately all the variables.To this end, the aim of this paper consists of presenting two Bayesian network models for traffic estimation, trying to bring a new tool to the transportation field.The first one deals with the problem of link flows, trip matrix estimation and traffic counting location and in the second one we propose a Bayesian network for route flow estimation (and hence link flows and OD flows) using data from plate scanning technique together with a model for optimal plate scanning device location.Since a Gaussian Bayesian network is used, these models allow us to update the predictions from a small subset of real data and probability intervals or regions are obtained to get an idea of the associated uncertainties.In addition dealing with data from the plate scanning approach we improve the under-specification level of the traffic flow estimation problem. Some background on Bayesian network modelsA Bayesian network (see, (Castillo et al., 1999)) is a pair (G, P ), where G is a directed acyclic graph (DAG) defined on a set of nodes X (the random variables), and P = {p(x 1 |π 1 ), . . ., p(x n |π n )} is a set of n conditional probability densities (CPD), one for each variable, and Π i is the set of parents of node X i in G.The set P defines the associated joint 19 www.intechopen.comBayesian Network 318 probability density of all nodes as p(1)The graph G contains all the qualitative information about the relationships among the variables, no matter which probability values are assigned to them 1 .Complementary, the probabilities in P contain the quantitative information, i.e., they complement the qualitative properties revealed by the graphical structure.

This paper proposes the integration of probabilistic data streams and relational database by using Bayesian networks that is one of the most famous techniques for expressing uncertain contexts. A Bayesian network is expressed by the graphical model while relational data are expressed by relation. To integrate them we make the relational model as the unified model for its simplicity. A Bayesian network is modeled as an abstract data type in an object relational database, and we define signatures to extract a probabilistic relation from a Bayesian network. We provide a scheme to integrate a probabilistic relation and normal relations. To allow continual queries over streams for a Bayesian network, we introduce a new concept, lifespan.