Dongping Ren, Jianxi Guo, Xiaoli Hao · ITM Web of Conferences · 2022
Variable Elimination (VE) is the most basic one of many Bayesian network inference algorithms. The speed and complexity of reasoning mainly depend on the order of elimination. Finding the optimal elimination order is a Nondeterministic Polynomial Hard (NP-Hard) problem, which is often solved by heuristic search in practice. In order to improve the speed of reasoning of the variable elimination method, the minimum, maximum potential, minimum missing edge and minimum added complexity search methods are studied. The Asian network is taken as an example to analyze and calculate the complexity and elimination of the above search method. Meta-order, through MATLAB R2018a, the above different search methods were constructed and reasoned separately. Finally, the performance of the four search methods was compared by inference time analysis. The experimental results show that the minimum increase complexity search method is better than other search methods, and the average time consuming is at least 0.012s, which can speed up the reasoning process of Bayesian network.
Cited by 1Open access
Abolfazl Mehbodniya, Julian Webber, Ravi Kumar et al. · Advances in medical technologies and clinical practice book series · 2022
Recent surveys suggest that the majority of the world's population is unconcerned with their health. Aside from a hectic lifestyle, research reveals that stress is also a component in the development of many diseases. Sudden cardiac arrest and death (SCD) is a major public health concern that jeopardizes patient safety. As a result, detecting such illnesses only by ECG is difficult. The Bayesian Dirichlet equivalence score, AIC (akaike information criterion), and MDL (maximum description length) scores make up the variable-order Bayesian network (VOBN). On the basis of HRV (heart rate variability) acquired from ECG and using a hybrid classifier to identify SCD patients from normal patients, this study predicts sudden cardiac arrest before it occurs within 30 minutes. The validity of the suggested study is checked using the physionet database of cardiac patients and normal people, as well as the Cleveland dataset. The proposed method achieves 97.1% accuracy, 96.2% precision, 89.8% recall, 84.82% F1-score, 54.66% AUC, and 45.92% ROC, according to the results.
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Kunfu Wang, Wei Feng, Xing Li · DEStech Transactions on Computer Science and Engineering · 2021
In order to assist network administrators to assess network security risks, a new Bayesian model of network risk assessment method is proposed. Firstly, the model designs the quantitative method of attack revenue and attack cost index, introduces the atomic attack efficiency variable, and integrates the variable into the calculation of probability, obtains the prior risk probability of each node in the network, so as to carry out the static evaluation of network risk. Secondly, DNO_Alg of deleting node order is proposed to determine the order of eliminating elements, so that Bayesian model can be transformed into cluster tree. Finally, combined with the detected attacks, the cluster tree propagation algorithm is used to dynamically calculate the posterior risk probability of nodes, so as to evaluate the network risk in real time.
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Wang Shuang-cheng, Cuiping Leng, Liu Feng-xia · 2008
At present, the methods of learning Bayesian network are not fit for finding causal knowledge from data, or require causal order between variables. While in reality often there is no prior knowledge of variable causal order. In this paper, an effective and practical method of learning causal Bayesian network is presented to find causal knowledge from data. Firstly, a maximal likelihood tree is built from data. Then a causal tree is obtained by orienting the edges of the maximal likelihood tree. Finally, a causal Bayesian network can be established based on local search & scoring method by finding father nodes of a node.
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Yifan Wang, Shiyu Liu, Pengfei Kou et al. · International Conference on Mechanical Engineering, Measurement Control, and Instrumentation · 2021
State of health (SOH) estimation for power battery is critical for reliable and safe operation of electric vehicles (EVs). In this paper, we propose a novel SOH estimation method combing equivalent circuit model (ECM) and Bayesian network. Firstly, a Bayesian network for SOH estimation is constructed according to existing knowledge about battery degradation. Then variables in Bayesian network is estimated by applying recursive least square algorithm with forgetting factor on first-order RC ECM. Afterwards, the model is trained to obtain the conditional probability distribution for each variable in Bayesian network. Finally, the effectiveness and accuracy of the model is verified using battery aging data.
Cited by 1
XU Miao, WANG Huiling, LIANG Yi, QI Xiaolong, GAO Yang · SHILAP Revista de lepidopterología · 2023
Bayesian network receiving increasing attention from researchers because of its strong uncertainty reasoning ability and causal representability.Learning a Bayesian network structure from data is an NP-hard problem.Among them,for the problem that the K2 algorithm strongly depends on the topological order of variables,an improved K2 learning method TSK2 is proposed,which combines variable neighbor sets and v-structure information.The proposed method effectively reduces the search scale in the order space and avoids prematurely falling into local optimum.Specifically,inspired by the orientation rules of the constraint algorithm,the method reliably adjusts the in-order position of the neighbors of the sink with the help of the identified v-structure and neighbor set information.Secondly,inspired by the basic structure of the shell net,with the help of the variable neighbor set information,the optimal sequence is obtained by performing the search of the three basic structures of shun-connection,sub-connection,and confluence-connection to accurately correct the order positions of parent nodes and child nodes.Experimental results show that the accuracy of the proposed algorithm is significantly improved compared with the comparison methods on the Asia and Alarm network datasets.A more accurate network structure can be learned.
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Fabrizio Riguzzi, Nicola Di Mauro · 2013
In order to apply the Information Bottleneck (IB) to LPADs, the network Gout is the result of the translation of the LPAD for which we want to learn the parameters plus the addition of the Y variable. The set of hidden variables contains the vector of the choice variables CH plus those atoms that are unobserved in the data, let us call them T. With X we indicate the set of atom variables that are observed in the data. Suppose you want to learn the parameters of an LPAD using IB. Consider the LPAD L: r1 = x1: 0.4∨x2: 0.3. r2 = x2: 0.1∨x3: 0.2. r3 = x4: 0.6∨x5: 0.4 ← x1. r4 = x5: 0.4 ← x2,x3. r5 = x6: 0.3∨x7: 0.2 ← x2,x5. The Bayesian network equivalent to L is shown in Figure 1. In order to apply IB to LPADs, the Fig.1. Bayesian network network Gout is the result of the translation of the LPAD for which we want to learn the parameters plus the addition of the Y variable. For the Gin network, we consider a naive Bayes factorization:
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Felipe S. Costa, Maria Marlene de Souza Pires, Sílvia Modesto Nassar · Journal of Computer Science · 2013
The nave Bayes classifier is considered one of the most effective classification algorithms today, competing with more modern and sophisticated classifiers. Despite being based on unrealistic (nave) assumption that all variables are independent, given the output class, the classifier provides proper results. However, depending on the scenario utilized (network structure, number of samples or training cases, number of variables), the network may not provide appropriate results. This study uses a process variable selection, using the chi-squared test to verify the existence of dependence between variables in the data model in order to identify the reasons which prevent a Bayesian network to provide good performance. A detailed analysis of the data is also proposed, unlike other existing work, as well as adjustments in case of limit values between two adjacent classes. Furthermore, variable weights are used in the calculation of a posteriori probabilities, calculated with mutual information function. Tests were applied in both a nave Bayesian network and a hierarchical Bayesian network. After testing, a significant reduction in error rate has been observed. The nave Bayesian network presented a drop in error rates from twenty five percent to five percent, considering the initial results of the classification process. In the hierarchical network, there was not only a drop in fifteen percent error rate, but also the final result came to zero.
Cited by 6Open access
Yuling Li, WU Qi-zong · 2007
Approximate inferring approach of Credal network based on Ant Colony Algorithms is put forward. Considering network inferring of goal-oriented in Bayesian network for the variable decision-maker is interested in given some evidence, the paper gives arithmetic for acquiring equivalent Credal network structure of goal-oriented. Selecting of these vertexes in Credal network is considered as a multistage decision-making. Based on this, Ant Colony Algorithms is applied for Credal network approximate inferring to reuse the vertexes of high probability of each variable in order to improve efficiency of inferring arithmetic and avoid some unnecessary computation. Finally, it shows the validity of the approach by simple analysis for a complex Credal network model.
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Ann‐Kristin Becker, Marcus Dörr, Stephan B. Felix et al. · PLoS Computational Biology · 2021
In this work, we introduce an entirely data-driven and automated approach to reveal disease-associated biomarker and risk factor networks from heterogeneous and high-dimensional healthcare data. Our workflow is based on Bayesian networks, which are a popular tool for analyzing the interplay of biomarkers. Usually, data require extensive manual preprocessing and dimension reduction to allow for effective learning of Bayesian networks. For heterogeneous data, this preprocessing is hard to automatize and typically requires domain-specific prior knowledge. We here combine Bayesian network learning with hierarchical variable clustering in order to detect groups of similar features and learn interactions between them entirely automated. We present an optimization algorithm for the adaptive refinement of such group Bayesian networks to account for a specific target variable, like a disease. The combination of Bayesian networks, clustering, and refinement yields low-dimensional but disease-specific interaction networks. These networks provide easily interpretable, yet accurate models of biomarker interdependencies. We test our method extensively on simulated data, as well as on data from the Study of Health in Pomerania (SHIP-TREND), and demonstrate its effectiveness using non-alcoholic fatty liver disease and hypertension as examples. We show that the group network models outperform available biomarker scores, while at the same time, they provide an easily interpretable interaction network.
Cited by 16Open access
Beáta Reiz, Lehel Csató, D. Dumitrescu · 2008
Bayesian networks encode causal relations between variables using probability and graph theory. We employ genetic algorithm to exploit these causal relations from data for classification problems, thus restricting the search space from directed acyclic graphs to trees. Prufer number encoding of the structure is employed for the representation of individuals in the genetic algorithm. Several score functions - information criteria - are also employed in order to analyse Prufer number encoding for Bayesian network structure learning. In this work we show that Prufer number encoding can reveal the causal dependence between class the variable and the attributes, the dependence being made without a-priori information regarding about the class variable.
Cited by 3
Luxian Fang · 2018
In the simulation of traditional physical model of electrical impedance scanning imaging (PMEISI), a physical model of electrical impedance scanning imaging (PMEISI) based on Bayesian network knowledge synthesis algorithm is proposed. The physical model uses the threshold as a variable, combines the synthesis threshold, and depends on the maximum between-class variance and the maximum peak signal to noise ratio (PSNR) criteria to establish a PMEISI and take into account the accuracy and noise immunity of the Bayesian network knowledge synthesis algorithm; in order to avoid the increase of the threshold affecting the efficiency of the algorithm, the Bayesian network knowledge synthesis algorithm is introduced into the physical model. Experiments show that the physical model has the advantages of accurate synthesis, strong noise immunity, good robustness, and more universality for the electrical impedance scanning imaging with different noises.
Cited by 1
HU QiGuo, DU ChunChao, CAO LiJie et al. · SHILAP Revista de lepidopterología · 2022
In order to solve the limitations of traditional methods in the reliability assessment of complex systems with multi-states and difficult to obtain accurate failure rates, and the problems of T-S fault tree in the system reliability analysis, such as complex calculation and inverse reasoning, etc., a reliability assessment method based on T-S fault tree and interval-valued fuzzy multi-state Bayesian network is proposed. Based on the analysis of the T-S fault tree, it is mapped into a Bayesian network. In the existing fuzzy Bayesian network reliability analysis method, the interval variable is introduced. Fuzzy processing is carried out to construct an interval-valued triangular fuzzy Bayesian network. Combining the characteristics of interval fuzzy subsets and Bayesian networks, a solution algorithm for leaf node failure probability, interval fuzzy importance, and interval fuzzy posterior probability is obtained under the condition of knowing only the root node failure status. Finally, the method is used to evaluate the reliability of the expansion system of the tunnel stacker, and it is verified that this method can accurately and effectively identify the weak links of the polymorphic system, and provide guidance for maintenance and diagnosis.
Cited by 0Open access
Dino Dittrich · Data Archiving and Networked Services (DANS) · 2018
People do not live in isolation. Instead, we constantly interact with others, which affects our actions, opinions, or well-being. Throughout the last decades, the network autocorrelation model has been the workhorse for modeling network influence on individual behavior. In the network autocorrelation model, actor observations for a variable of interest are allowed to be correlated, where a network autocorrelation parameter represents and quantifies the strength of a network influence on the variable of interest. More precisely, an actor’s observation is assumed to be a function not only of a set of explanatory variables but also of the observations for the actor's neighbors, i.e., other actors in the network this actor is tied to. In this thesis, we develop a fully Bayesian framework to estimate the network autocorrelation model and to test multiple hypotheses on the network autocorrelation parameter(s) against each other. Taking the Bayesian route hereto has at least three attractive features that are not shared by classical statistical methods such as maximum likelihood estimation and null hypothesis significance testing. First, the Bayesian approach enables researchers to include previous empirical information about the network autocorrelation parameter through a prior distribution, which may attenuate the underestimation of the network autocorrelation parameter associated with maximum likelihood estimation of the model. Concomitantly, we also derive Bayesian default procedures for situations in which such prior information is completely unavailable. Second, Bayesian techniques do not rely on asymptotic approximations when estimating uncertainty and performing inference about the network autocorrelation parameter but yield accurate results even in case of small networks. Third, using Bayes factors as opposed to null hypothesis significance testing, researchers can test any number of hypotheses on the network autocorrelation parameter and quantify the amount of relative evidence in the data for each tested hypothesis. We provide several such Bayes factors and generalize the presented methodology to test order hypotheses on multiple network autocorrelation parameters, representing the strength of multiple influence mechanisms that may have some connection to the variable of interest. Furthermore, we introduce a discrete exponential family model to analyze network autocorrelated count data for which the network autocorrelation model itself is not well-suited. This novel model permits principled statistical inference without making any potentially limiting distributional assumptions on the marginal or conditional counts but is flexible enough to accommodate a wide range of count patterns. In sum, the methods developed in this thesis allow researchers studying network influence to quantify and test the strength of network influence(s) on a variable of interest in ways that go beyond the current state of the art.
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Ta Sarah Borys · 2009
A “Bayesian network ” (BN) is a graph in which every node represents a random variable, and edges represent stochastic dependence. Fig. 1, for example, is a graphical representation of the following joint probability: p(a, b, c, d, e, f) = p(a)p(b|a)p(c|a)p(d|b, c)p(e|c)p(f |c) (1) A “dynamic Bayesian network ” (DBN) is a network that can dynamically change its size. In a hidden Markov model, for example, in order to recognize an audio file of T frames, we need to compute the values of T hidden state variables, q1,..., qT. The state variables q2 and q3 are usually structurally identical; they depend on similar context variables, only shifted by one frame. Structures of this kind can be represented by allowing the network to dynamically “unroll ” in order to create T consecutive state variables. Fig. 2, copied from the GMTK book
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Seung-Bin Im, Keum-Sung Hwang, Sung-Bae Cho · 2007
For a robot to understand a scene, we have to infer and extract meaningful information from vision sensor data. Since scene understanding consists in recognizing several visual contexts, we have to extract these contextual cues and understand their relationships. However, context extraction from visual information is difficult due to uncertain information in variable environments, imperfect nature of the feature extraction methods and high computational complexity of reasoning from the complex relationship. In order to manage the uncertainties effectively, in this paper, we adopted Bayesian probabilistic approach, and proposed a Bayesian network framework that synthesizes the low level features and the high level semantic cues. It contains how to develop and utilize an integrated Bayesian network model. In the experimental results of two applications, the efficacy of the proposed framework is shown.
Cited by 2
Hatim Alsuwat, Emad Alsuwat, Marco Valtorta et al. · 2019
Concept drift is a significant challenge that greatly influences the accuracy and reliability of machine learning models. There is, therefore, a need to detect concept drift in order to ensure the validity of learned models. In this research, we study the issue of concept drift in the context of discrete Bayesian networks. We propose a probabilistic graphical model framework to explicitly detect the presence of concept drift using latent variables. We employ latent variables to model real concept drift and uncertainty drift over time. For modeling real concept drift, we propose to monitor the mean of the distribution of the latent variable over time. For modeling uncertainty drift, we suggest to monitor the change in beliefs of the latent variable over time, i.e., we monitor the maximum value that the probability density function of the distribution takes over time. We implement our proposed framework and present our empirical results using two of the most commonly used Bayesian networks in Bayesian experiments, namely the Burglary-Earthquake Network and the Chest Clinic network.
Cited by 1Open access
Limin Wang, Haoyu Zhao · Entropy · 2015
As one of the most common types of graphical models, the Bayesian classifier has become an extremely popular approach to dealing with uncertainty and complexity. The scoring functions once proposed and widely used for a Bayesian network are not appropriate for a Bayesian classifier, in which class variable C is considered as a distinguished one. In this paper, we aim to clarify the working mechanism of Bayesian classifiers from the perspective of the chain rule of joint probability distribution. By establishing the mapping relationship between conditional probability distribution and mutual information, a new scoring function, Sum_MI, is derived and applied to evaluate the rationality of the Bayesian classifiers. To achieve global optimization and high dependence representation, the proposed learning algorithm, the flexible K-dependence Bayesian (FKDB) classifier, applies greedy search to extract more information from the K-dependence network structure. Meanwhile, during the learning procedure, the optimal attribute order is determined dynamically, rather than rigidly. In the experimental study, functional dependency analysis is used to improve model interpretability when the structure complexity is restricted.
Cited by 10Open access
2008
We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and parameters can be learned efficiently, even without restricting the size of the parent variable sets. We then consider the problem of optimizing the variable order for a given set of features. This is still a computationally hard problem, but we present a convex relaxation that yields an optimal “soft” ordering in polynomial time. One novel aspect of the approach is that we do not perform a discrete search over DAG structures, nor over variable orders, but instead solve a continuous convex relaxation that can then be rounded to obtain a valid network structure. We conduct an experimental comparison against standard structure search procedures over standard objectives, which cope with local minima, and evaluate the advantages of using convex relaxations that reduce the effects of local minima. 1
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Yong Dai, Qianru Wang, Zhibo Wang et al. · 2018
In order to solve the uncertain multivariable decision-making problem in hydro power output, Bayesian network method is introduced into the risk assessment of hydro power participating in large-scale direct purchase of electricity. By analyzing the relationship between the variables in the case system, a Bayesian network model describing the relationship of uncertainties among the variables is constructed, including a directed acyclic graph representing its dependence and a conditional probability table representing its specific probability dependence. Probabilistic reasoning is done on the premise that the target variable, that is, the hydro power output, achieves the expected goal. The results of the example show that when the precipitation is 50 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">~</sub> 100mm, the target variable can reach the optimal value, so the minimum risk and the risk interval of hydro power participation in large direct electricity purchase are determined. The Bayesian network graphically expresses the uncertainty relationship between variables in the case system. The result of probabilistic reasoning takes into account both the seasons and the climate factors, so that the expected targets are optimally and effectively solved Multivariable decision problems with uncertainties in hydro power output.
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