The use of dynamic programming(DP)algorithms to learn Bayesian network structures is limited by their high space complexity and difficulty in learning the structure of large-scale networks.Therefore,this study propose...The use of dynamic programming(DP)algorithms to learn Bayesian network structures is limited by their high space complexity and difficulty in learning the structure of large-scale networks.Therefore,this study proposes a DP algorithm based on node block sequence constraints.The proposed algorithm constrains the traversal process of the parent graph by using the M-sequence matrix to considerably reduce the time consumption and space complexity by pruning the traversal process of the order graph using the node block sequence.Experimental results show that compared with existing DP algorithms,the proposed algorithm can obtain learning results more efficiently with less than 1%loss of accuracy,and can be used for learning larger-scale networks.展开更多
Ordering based search methods have advantages over graph based search methods for structure learning of Bayesian networks in terms on the efficiency. With the aim of further increasing the accuracy of ordering based s...Ordering based search methods have advantages over graph based search methods for structure learning of Bayesian networks in terms on the efficiency. With the aim of further increasing the accuracy of ordering based search methods, we first propose to increase the search space, which can facilitate escaping from the local optima. We present our search operators with majorizations, which are easy to implement. Experiments show that the proposed algorithm can obtain significantly more accurate results. With regard to the problem of the decrease on efficiency due to the increase of the search space, we then propose to add path priors as constraints into the swap process. We analyze the coefficient which may influence the performance of the proposed algorithm, the experiments show that the constraints can enhance the efficiency greatly, while has little effect on the accuracy. The final experiments show that, compared to other competitive methods, the proposed algorithm can find better solutions while holding high efficiency at the same time on both synthetic and real data sets.展开更多
In view of the shortcomings of traditional Bayesian network(BN)structure learning algorithm,such as low efficiency,premature algorithm and poor learning effect,the intelligent algorithm of cuckoo search(CS)and particl...In view of the shortcomings of traditional Bayesian network(BN)structure learning algorithm,such as low efficiency,premature algorithm and poor learning effect,the intelligent algorithm of cuckoo search(CS)and particle swarm optimization(PSO)is selected.Combined with the characteristics of BN structure,a BN structure learning algorithm of CS-PSO is proposed.Firstly,the CS algorithm is improved from the following three aspects:the maximum spanning tree is used to guide the initialization direction of the CS algorithm,the fitness of the solution is used to adjust the optimization and abandoning process of the solution,and PSO algorithm is used to update the position of the CS algorithm.Secondly,according to the structure characteristics of BN,the CS-PSO algorithm is applied to the structure learning of BN.Finally,chest clinic,credit and car diagnosis classic network are utilized as the simulation model,and the modeling and simulation comparison of greedy algorithm,K2 algorithm,CS algorithm and CS-PSO algorithm are carried out.The results show that the CS-PSO algorithm has fast convergence speed,high convergence accuracy and good stability in the structure learning of BN,and it can get the accurate BN structure model faster and better.展开更多
With the rapid development of the 5G communications,the edge intelligence enables Internet of Vehicles(IoV)to provide traffic forecasting to alleviate traffic congestion and improve quality of experience of users simu...With the rapid development of the 5G communications,the edge intelligence enables Internet of Vehicles(IoV)to provide traffic forecasting to alleviate traffic congestion and improve quality of experience of users simultaneously.To enhance the forecasting performance,a novel edge-enabled probabilistic graph structure learning model(PGSLM)is proposed,which learns the graph structure and parameters by the edge sensing information and discrete probability distribution on the edges of the traffic road network.To obtain the spatio-temporal dependencies of traffic data,the learned dynamic graphs are combined with a predefined static graph to generate the graph convolution part of the recurrent graph convolution module.During the training process,a new graph training loss is introduced,which is composed of the K nearest neighbor(KNN)graph constructed by the traffic feature tensors and the graph structure.Detailed experimental results show that,compared with existing models,the proposed PGSLM improves the traffic prediction performance in terms of average absolute error and root mean square error in IoV.展开更多
To obtain the optimal Bayesian network(BN)structure,researchers often use the hybrid learning algorithm that combines the constraint-based(CB)method and the score-and-search(SS)method.This hybrid method has the proble...To obtain the optimal Bayesian network(BN)structure,researchers often use the hybrid learning algorithm that combines the constraint-based(CB)method and the score-and-search(SS)method.This hybrid method has the problemthat the search efficiency could be improved due to the ample search space.The search process quickly falls into the local optimal solution,unable to obtain the global optimal.Based on this,the Particle SwarmOptimization(PSO)algorithm based on the search space constraint process is proposed.In the first stage,the method uses dynamic adjustment factors to constrain the structure search space and enrich the diversity of the initial particles.In the second stage,the update mechanism is redefined,so that each step of the update process is consistent with the current structure which forms a one-to-one correspondence.At the same time,the“self-awakened”mechanism is added to prevent precocious particles frombeing part of the best.After the fitness value of the particle converges prematurely,the activation operation makes the particles jump out of the local optimal values to prevent the algorithmfromconverging too quickly into the local optimum.Finally,the standard network dataset was compared with other algorithms.The experimental results showed that the algorithmcould find the optimal solution at a small number of iterations and a more accurate network structure to verify the algorithm’s effectiveness.展开更多
In recent years,the development of machine learning has introduced new analytical methods to theoretical research,one of which is Bayesian network—a probabilistic graphical model well-suited for modelling complex non...In recent years,the development of machine learning has introduced new analytical methods to theoretical research,one of which is Bayesian network—a probabilistic graphical model well-suited for modelling complex non-deterministic systems.A recent study has revealed that the order in which variables are read from data can impact the structure of a Bayesian network(Kitson and Constantinou in The impact of variable ordering on Bayesian Network Structure Learning,2022.arXiv preprint arXiv:2206.08952).However,in empirical studies,the variable order in a dataset is often arbitrary,leading to unreliable results.To address this issue,this study proposed a hybrid method that combined theory-driven and data-driven approaches to mitigate the impact of variable ordering on the learning of Bayesian network structures.The proposed method was illustrated using an empirical study predicting depression and aggressive behavior in high school students.The results demonstrated that the obtained Bayesian network structure is robust to variable orders and theoretically interpretable.The commonalities and specificities in the network structure of depression and aggressive behavior are both in line with theorical expectations,providing empirical evidence for the validity of the hybrid method.展开更多
Recommendation systems play a crucial role in uncovering concealed interactions among users and items within online social networks.Recently,Graph Neural Network(GNN)-based recommendation systems exploit higher-order ...Recommendation systems play a crucial role in uncovering concealed interactions among users and items within online social networks.Recently,Graph Neural Network(GNN)-based recommendation systems exploit higher-order interactions within the user-item interaction graph,demonstrating cutting-edge performance in recommendation tasks.However,GNN-based recommendation models are susceptible to different types of noise attacks,such as deliberate perturbations or false clicks.These attacks propagate through the graph and adversely affect the robustness of recommendation results.Conventional two-stage method that purifies the graph before training the GNN model is suboptimal.To strengthen the model’s resilience to noise,we propose Graph Structure Learning for Robust Recommendation(GSLRRec),a joint learning framework that integrates graph structure learning and GNN model training for recommendation.Specifically,GSLRRec considers the graph adjacency matrix as adjustable parameters,and simultaneously optimizes both the graph structure and the representations of user/item nodes for recommendation.During the joint training process,the graph structure learning employs low-rank and sparse constraints to effectively denoise the graph.Our experiments illustrate that the simultaneous learning of both structure and GNN parameters can provide more robust recommendation results under various noise levels.展开更多
Finding out reasonable structures from bulky data is one of the difficulties in modeling of Bayesian network （BN）, which is also necessary in promoting the application of BN. This pa- per proposes an immune algorith...Finding out reasonable structures from bulky data is one of the difficulties in modeling of Bayesian network （BN）, which is also necessary in promoting the application of BN. This pa- per proposes an immune algorithm based method （BN-IA） for the learning of the BN structure with the idea of vaccination. Further- more, the methods on how to extract the effective vaccines from local optimal structure and root nodes are also described in details. Finally, the simulation studies are implemented with the helicopter convertor BN model and the car start BN model. The comparison results show that the proposed vaccines and the BN-IA can learn the BN structure effectively and efficiently.展开更多
Node order is one of the most important factors in learning the structure of a Bayesian network(BN)for probabilistic reasoning.To improve the BN structure learning,we propose a node order learning algorithmbased on th...Node order is one of the most important factors in learning the structure of a Bayesian network(BN)for probabilistic reasoning.To improve the BN structure learning,we propose a node order learning algorithmbased on the frequently used Bayesian information criterion(BIC)score function.The algorithm dramatically reduces the space of node order and makes the results of BN learning more stable and effective.Specifically,we first find the most dependent node for each individual node,prove analytically that the dependencies are undirected,and then construct undirected subgraphs UG.Secondly,the UG-is examined and connected into a single undirected graph UGC.The relation between the subgraph number and the node number is analyzed.Thirdly,we provide the rules of orienting directions for all edges in UGC,which converts it into a directed acyclic graph(DAG).Further,we rank the DAG’s topology order and describe the BIC-based node order learning algorithm.Its complexity analysis shows that the algorithm can be conducted in linear time with respect to the number of samples,and in polynomial time with respect to the number of variables.Finally,experimental results demonstrate significant performance improvement by comparing with other methods.展开更多
Learning structure from data is one of the most important fundamental tasks of Bayesian network research. Particularly, learning optional structure of Bayesian network is a non-deterministic polynomial-time （NP） har...Learning structure from data is one of the most important fundamental tasks of Bayesian network research. Particularly, learning optional structure of Bayesian network is a non-deterministic polynomial-time （NP） hard problem. To solve this problem, many heuristic algorithms have been proposed, and some of them learn Bayesian network structure with the help of different types of prior knowledge. However, the existing algorithms have some restrictions on the prior knowledge, such as quality restriction and use restriction. This makes it di？cult to use the prior knowledge well in these algorithms. In this paper, we introduce the prior knowledge into the Markov chain Monte Carlo （MCMC） algorithm and propose an algorithm called Constrained MCMC （C-MCMC） algorithm to learn the structure of the Bayesian network. Three types of prior knowledge are defined： existence of parent node, absence of parent node, and distribution knowledge including the conditional probability distribution （CPD） of edges and the probability distribution （PD） of nodes. All of these types of prior knowledge are easily used in this algorithm. We conduct extensive experiments to demonstrate the feasibility and effectiveness of the proposed method C-MCMC.展开更多
Node classification has a wide range of application scenarios such as citation analysis and social network analysis.In many real-world attributed networks,a large portion of classes only contain limited labeled nodes....Node classification has a wide range of application scenarios such as citation analysis and social network analysis.In many real-world attributed networks,a large portion of classes only contain limited labeled nodes.Most of the existing node classification methods cannot be used for few-shot node classification.To train the model effectively and improve the robustness and reliability of the model with scarce labeled samples,in this paper,we propose a local adaptive discriminant structure learning(LADSL)method for few-shot node classification.LADSL aims to properly represent the nodes in the attributed graphs and learn a metric space with a strong discriminating power by reducing the intra-class variations and enlargingginter-classdifferences.Extensiveexperiments conducted on various attributed networks datasets demonstrate that LADSL is superior to the other methods on few-shot node classification task.展开更多
In this paper, we propose a more efficient Bayesian network structure learning algorithm under the framework of score based local learning （SLL）. Our algorithm significantly improves computational efficiency by rest...In this paper, we propose a more efficient Bayesian network structure learning algorithm under the framework of score based local learning （SLL）. Our algorithm significantly improves computational efficiency by restricting the neighbors of each variable to a small subset of candidates and storing necessary information to uncover the spouses, at the same time guaranteeing to find the optimal neighbor set in the same sense as SLL. The algorithm is the- oretically sound in the sense that it is optimal in the limit of large sample size. Empirical results testify its improved speed without loss of quality in the learned structures.展开更多
How to improve the efficiency of exact learning of the Bayesian network structure is a challenging issue.In this paper,four different causal constraints algorithms are added into score calculations to prune possible p...How to improve the efficiency of exact learning of the Bayesian network structure is a challenging issue.In this paper,four different causal constraints algorithms are added into score calculations to prune possible parent sets,improving state-ofthe-art learning algorithms’efficiency.Experimental results indicate that exact learning algorithms can significantly improve the efficiency with only a slight loss of accuracy.Under causal constraints,these exact learning algorithms can prune about 70%possible parent sets and reduce about 60%running time while only losing no more than 2%accuracy on average.Additionally,with sufficient samples,exact learning algorithms with causal constraints can also obtain the optimal network.In general,adding max-min parents and children constraints has better results in terms of efficiency and accuracy among these four causal constraints algorithms.展开更多
Bayesian network is a popular approach to uncertainty knowledge representation and reasoning. Structure learning is the first step to learn a Bayesian network. Score-based methods are one of the most popular ways of l...Bayesian network is a popular approach to uncertainty knowledge representation and reasoning. Structure learning is the first step to learn a Bayesian network. Score-based methods are one of the most popular ways of learning the structure. In most cases, the score of Bayesian network is defined as adding the log-likelihood score and complexity score by using the penalty function. If the penalty function is set unreasonably, it may hurt the performance of structure search. Thus, Bayesian network structure learning is essentially a bi-objective optimization problem. However, the existing bi-objective structure learning algorithms can only be applied to small-scale networks. To this end, this paper proposes a bi-objective evolutionary Bayesian network structure learning algorithm via skeleton constraint (BBS) for the medium-scale networks. To boost the performance of searching, BBS introduces the random order prior (ROP) initial operator. ROP generates a skeleton to constrain the searching space, which is the key to expanding the scale of structure learning problems. Then, the acyclic structures are guaranteed by adding the orders of variables in the initial skeleton. After that, BBS designs the Pareto rank based crossover and skeleton guided mutation operators. The operators operate on the skeleton obtained in ROP to make the search more targeted. Finally, BBS provides a strategy to choose the final solution. The experimental results show that BBS can always find the structure which is closer to the ground truth compared with the single-objective structure learning methods. Furthermore, compared with the existing bi-objective structure learning methods, BBS is scalable and can be applied to medium-scale Bayesian network datasets. On the educational problem of discovering the influencing factors of students’ academic performance, BBS provides higher quality solutions and is featured with the flexibility of solution selection compared with the widely-used Bayesian network structure learning methods.展开更多
At present Bayesian Networks(BN)are being used widely for demonstrating uncertain knowledge in many disciplines,including biology,computer science,risk analysis,service quality analysis,and business.But they suffer fr...At present Bayesian Networks(BN)are being used widely for demonstrating uncertain knowledge in many disciplines,including biology,computer science,risk analysis,service quality analysis,and business.But they suffer from the problem that when the nodes and edges increase,the structure learning difficulty increases and algorithms become inefficient.To solve this problem,heuristic optimization algorithms are used,which tend to find a near-optimal answer rather than an exact one,with particle swarm optimization(PSO)being one of them.PSO is a swarm intelligence-based algorithm having basic inspiration from flocks of birds(how they search for food).PSO is employed widely because it is easier to code,converges quickly,and can be parallelized easily.We use a recently proposed version of PSO called generalized particle swarm optimization(GEPSO)to learn bayesian network structure.We construct an initial directed acyclic graph(DAG)by using the max-min parent’s children(MMPC)algorithm and cross relative average entropy.ThisDAGis used to create a population for theGEPSO optimization procedure.Moreover,we propose a velocity update procedure to increase the efficiency of the algorithmic search process.Results of the experiments show that as the complexity of the dataset increases,our algorithm Bayesian network generalized particle swarm optimization(BN-GEPSO)outperforms the PSO algorithm in terms of the Bayesian information criterion(BIC)score.展开更多
In soft sensor field, just-in-time learning(JITL) is an effective approach to model nonlinear and time varying processes. However, most similarity criterions in JITL are computed in the input space only while ignoring...In soft sensor field, just-in-time learning(JITL) is an effective approach to model nonlinear and time varying processes. However, most similarity criterions in JITL are computed in the input space only while ignoring important output information, which may lead to inaccurate construction of relevant sample set. To solve this problem, we propose a novel supervised feature extraction method suitable for the regression problem called supervised local and non-local structure preserving projections(SLNSPP), in which both input and output information can be easily and effectively incorporated through a newly defined similarity index. The SLNSPP can not only retain the virtue of locality preserving projections but also prevent faraway points from nearing after projection,which endues SLNSPP with powerful discriminating ability. Such two good properties of SLNSPP are desirable for JITL as they are expected to enhance the accuracy of similar sample selection. Consequently, we present a SLNSPP-JITL framework for developing adaptive soft sensor, including a sparse learning strategy to limit the scale and update the frequency of database. Finally, two case studies are conducted with benchmark datasets to evaluate the performance of the proposed schemes. The results demonstrate the effectiveness of LNSPP and SLNSPP.展开更多
A new method to evaluate the fitness of the Bayesian networks according to the observed data is provided. The main advantage of this criterion is that it is suitable for both the complete and incomplete cases while th...A new method to evaluate the fitness of the Bayesian networks according to the observed data is provided. The main advantage of this criterion is that it is suitable for both the complete and incomplete cases while the others not. Moreover it facilitates the computation greatly. In order to reduce the search space, the notation of equivalent class proposed by David Chickering is adopted. Instead of using the method directly, the novel criterion, variable ordering, and equivalent class are combined,moreover the proposed mthod avoids some problems caused by the previous one. Later, the genetic algorithm which allows global convergence, lack in the most of the methods searching for Bayesian network is applied to search for a good model in thisspace. To speed up the convergence, the genetic algorithm is combined with the greedy algorithm. Finally, the simulation shows the validity of the proposed approach.展开更多
Structure learning of Bayesian networks is a wellresearched but computationally hard task.For learning Bayesian networks,this paper proposes an improved algorithm based on unconstrained optimization and ant colony opt...Structure learning of Bayesian networks is a wellresearched but computationally hard task.For learning Bayesian networks,this paper proposes an improved algorithm based on unconstrained optimization and ant colony optimization（U-ACO-B） to solve the drawbacks of the ant colony optimization（ACO-B）.In this algorithm,firstly,an unconstrained optimization problem is solved to obtain an undirected skeleton,and then the ACO algorithm is used to orientate the edges,thus returning the final structure.In the experimental part of the paper,we compare the performance of the proposed algorithm with ACO-B algorithm.The experimental results show that our method is effective and greatly enhance convergence speed than ACO-B algorithm.展开更多
We propose an approach for dependence tree structure learning via copula. A nonparametric algorithm for copula estimation is presented. Then a Chow-Liu like method based on dependence measure via copula is proposed to...We propose an approach for dependence tree structure learning via copula. A nonparametric algorithm for copula estimation is presented. Then a Chow-Liu like method based on dependence measure via copula is proposed to estimate maximum spanning bivariate copula associated with bivariate dependence relations. The main advantage of the approach is that learning with empirical copula focuses on dependence relations among random variables, without the need to know the properties of individual variables as well as without the requirement to specify parametric family of entire underlying distribution for individual variables. Experiments on two real-application data sets show the effectiveness of the proposed method.展开更多
Learning Bayesian network structure is one of the most important branches in Bayesian network. The most popular graphical representative of a Bayesian network structure is an essential graph. This paper shows a combin...Learning Bayesian network structure is one of the most important branches in Bayesian network. The most popular graphical representative of a Bayesian network structure is an essential graph. This paper shows a combined algorithm according to the three rules for finding the essential graph of a given directed acyclic graph. Moreover, the complexity and advantages of this combined algorithm over others are also discussed. The aim of this paper is to present the proof of the correctness of the combined algorithm.展开更多
基金Shaanxi Science Fund for Distinguished Young Scholars,Grant/Award Number:2024JC-JCQN-57Xi’an Science and Technology Plan Project,Grant/Award Number:2023JH-QCYJQ-0086+2 种基金Scientific Research Program Funded by Education Department of Shaanxi Provincial Government,Grant/Award Number:P23JP071Engineering Technology Research Center of Shaanxi Province for Intelligent Testing and Reliability Evaluation of Electronic Equipments,Grant/Award Number:2023-ZC-GCZX-00472022 Shaanxi University Youth Innovation Team Project。
文摘The use of dynamic programming(DP)algorithms to learn Bayesian network structures is limited by their high space complexity and difficulty in learning the structure of large-scale networks.Therefore,this study proposes a DP algorithm based on node block sequence constraints.The proposed algorithm constrains the traversal process of the parent graph by using the M-sequence matrix to considerably reduce the time consumption and space complexity by pruning the traversal process of the order graph using the node block sequence.Experimental results show that compared with existing DP algorithms,the proposed algorithm can obtain learning results more efficiently with less than 1%loss of accuracy,and can be used for learning larger-scale networks.
基金supported by the National Natural Science Fundation of China(61573285)the Doctoral Fundation of China(2013ZC53037)
文摘Ordering based search methods have advantages over graph based search methods for structure learning of Bayesian networks in terms on the efficiency. With the aim of further increasing the accuracy of ordering based search methods, we first propose to increase the search space, which can facilitate escaping from the local optima. We present our search operators with majorizations, which are easy to implement. Experiments show that the proposed algorithm can obtain significantly more accurate results. With regard to the problem of the decrease on efficiency due to the increase of the search space, we then propose to add path priors as constraints into the swap process. We analyze the coefficient which may influence the performance of the proposed algorithm, the experiments show that the constraints can enhance the efficiency greatly, while has little effect on the accuracy. The final experiments show that, compared to other competitive methods, the proposed algorithm can find better solutions while holding high efficiency at the same time on both synthetic and real data sets.
基金National Natural Science Foundation of China(Nos.61164010,61233003)。
文摘In view of the shortcomings of traditional Bayesian network(BN)structure learning algorithm,such as low efficiency,premature algorithm and poor learning effect,the intelligent algorithm of cuckoo search(CS)and particle swarm optimization(PSO)is selected.Combined with the characteristics of BN structure,a BN structure learning algorithm of CS-PSO is proposed.Firstly,the CS algorithm is improved from the following three aspects:the maximum spanning tree is used to guide the initialization direction of the CS algorithm,the fitness of the solution is used to adjust the optimization and abandoning process of the solution,and PSO algorithm is used to update the position of the CS algorithm.Secondly,according to the structure characteristics of BN,the CS-PSO algorithm is applied to the structure learning of BN.Finally,chest clinic,credit and car diagnosis classic network are utilized as the simulation model,and the modeling and simulation comparison of greedy algorithm,K2 algorithm,CS algorithm and CS-PSO algorithm are carried out.The results show that the CS-PSO algorithm has fast convergence speed,high convergence accuracy and good stability in the structure learning of BN,and it can get the accurate BN structure model faster and better.
基金supported by the project of the National Natural Science Foundation of China(No.61772562)the Knowledge Innovation Program of Wuhan-Basic Research(No.2022010801010225)the Fundamental Research Funds for the Central Universities(No.2662022YJ012)。
文摘With the rapid development of the 5G communications,the edge intelligence enables Internet of Vehicles(IoV)to provide traffic forecasting to alleviate traffic congestion and improve quality of experience of users simultaneously.To enhance the forecasting performance,a novel edge-enabled probabilistic graph structure learning model(PGSLM)is proposed,which learns the graph structure and parameters by the edge sensing information and discrete probability distribution on the edges of the traffic road network.To obtain the spatio-temporal dependencies of traffic data,the learned dynamic graphs are combined with a predefined static graph to generate the graph convolution part of the recurrent graph convolution module.During the training process,a new graph training loss is introduced,which is composed of the K nearest neighbor(KNN)graph constructed by the traffic feature tensors and the graph structure.Detailed experimental results show that,compared with existing models,the proposed PGSLM improves the traffic prediction performance in terms of average absolute error and root mean square error in IoV.
基金funded by the National Natural Science Foundation of China(62262016)in part by the Hainan Provincial Natural Science Foundation Innovation Research Team Project(620CXTD434)+1 种基金in part by the High-Level Talent Project Hainan Natural Science Foundation(620RC557)in part by the Hainan Provincial Key R&D Plan(ZDYF2021GXJS199).
文摘To obtain the optimal Bayesian network(BN)structure,researchers often use the hybrid learning algorithm that combines the constraint-based(CB)method and the score-and-search(SS)method.This hybrid method has the problemthat the search efficiency could be improved due to the ample search space.The search process quickly falls into the local optimal solution,unable to obtain the global optimal.Based on this,the Particle SwarmOptimization(PSO)algorithm based on the search space constraint process is proposed.In the first stage,the method uses dynamic adjustment factors to constrain the structure search space and enrich the diversity of the initial particles.In the second stage,the update mechanism is redefined,so that each step of the update process is consistent with the current structure which forms a one-to-one correspondence.At the same time,the“self-awakened”mechanism is added to prevent precocious particles frombeing part of the best.After the fitness value of the particle converges prematurely,the activation operation makes the particles jump out of the local optimal values to prevent the algorithmfromconverging too quickly into the local optimum.Finally,the standard network dataset was compared with other algorithms.The experimental results showed that the algorithmcould find the optimal solution at a small number of iterations and a more accurate network structure to verify the algorithm’s effectiveness.
基金supported by National Natural Science Foundation of China(Grant No.32171089)Research Fund from Hangzhou Mingshitang Education Technology Development Co.,Ltd.(Project No.1222000035).
文摘In recent years,the development of machine learning has introduced new analytical methods to theoretical research,one of which is Bayesian network—a probabilistic graphical model well-suited for modelling complex non-deterministic systems.A recent study has revealed that the order in which variables are read from data can impact the structure of a Bayesian network(Kitson and Constantinou in The impact of variable ordering on Bayesian Network Structure Learning,2022.arXiv preprint arXiv:2206.08952).However,in empirical studies,the variable order in a dataset is often arbitrary,leading to unreliable results.To address this issue,this study proposed a hybrid method that combined theory-driven and data-driven approaches to mitigate the impact of variable ordering on the learning of Bayesian network structures.The proposed method was illustrated using an empirical study predicting depression and aggressive behavior in high school students.The results demonstrated that the obtained Bayesian network structure is robust to variable orders and theoretically interpretable.The commonalities and specificities in the network structure of depression and aggressive behavior are both in line with theorical expectations,providing empirical evidence for the validity of the hybrid method.
基金supported by the National Natural Science Foundation of China(Nos.62272001 and 62206002)the Anhui Provincial Natural Science Foundation(No.2208085QF195)+2 种基金the Hefei Key Common Technology Project(No.GJ2022GX15)the University Collaborative Innovation Project of Anhui Province(No.GXXT-2021-087)the Anhui Province Key Research and Development Program(No.202104a05020058).
文摘Recommendation systems play a crucial role in uncovering concealed interactions among users and items within online social networks.Recently,Graph Neural Network(GNN)-based recommendation systems exploit higher-order interactions within the user-item interaction graph,demonstrating cutting-edge performance in recommendation tasks.However,GNN-based recommendation models are susceptible to different types of noise attacks,such as deliberate perturbations or false clicks.These attacks propagate through the graph and adversely affect the robustness of recommendation results.Conventional two-stage method that purifies the graph before training the GNN model is suboptimal.To strengthen the model’s resilience to noise,we propose Graph Structure Learning for Robust Recommendation(GSLRRec),a joint learning framework that integrates graph structure learning and GNN model training for recommendation.Specifically,GSLRRec considers the graph adjacency matrix as adjustable parameters,and simultaneously optimizes both the graph structure and the representations of user/item nodes for recommendation.During the joint training process,the graph structure learning employs low-rank and sparse constraints to effectively denoise the graph.Our experiments illustrate that the simultaneous learning of both structure and GNN parameters can provide more robust recommendation results under various noise levels.
基金supported by the National Natural Science Foundation of China(7110111671271170)+1 种基金the Program for New Century Excellent Talents in University(NCET-13-0475)the Basic Research Foundation of NPU(JC20120228)
文摘Finding out reasonable structures from bulky data is one of the difficulties in modeling of Bayesian network （BN）, which is also necessary in promoting the application of BN. This pa- per proposes an immune algorithm based method （BN-IA） for the learning of the BN structure with the idea of vaccination. Further- more, the methods on how to extract the effective vaccines from local optimal structure and root nodes are also described in details. Finally, the simulation studies are implemented with the helicopter convertor BN model and the car start BN model. The comparison results show that the proposed vaccines and the BN-IA can learn the BN structure effectively and efficiently.
基金The work partially supported by the National Natural Science Foundation of China(Grant Nos.61432011,U1435212,61322211 and 61672332)the Postdoctoral Science Foundation of China(2016M591409)+1 种基金the Natural Science Foundation of Shanxi Province,China(201801D121115 and 2013011016-4)Research Project Supported by Shanxi Scholarship Council of China(2020-095).
文摘Node order is one of the most important factors in learning the structure of a Bayesian network(BN)for probabilistic reasoning.To improve the BN structure learning,we propose a node order learning algorithmbased on the frequently used Bayesian information criterion(BIC)score function.The algorithm dramatically reduces the space of node order and makes the results of BN learning more stable and effective.Specifically,we first find the most dependent node for each individual node,prove analytically that the dependencies are undirected,and then construct undirected subgraphs UG.Secondly,the UG-is examined and connected into a single undirected graph UGC.The relation between the subgraph number and the node number is analyzed.Thirdly,we provide the rules of orienting directions for all edges in UGC,which converts it into a directed acyclic graph(DAG).Further,we rank the DAG’s topology order and describe the BIC-based node order learning algorithm.Its complexity analysis shows that the algorithm can be conducted in linear time with respect to the number of samples,and in polynomial time with respect to the number of variables.Finally,experimental results demonstrate significant performance improvement by comparing with other methods.
基金This work was supported by the National Natural Science Foundation of China under Grant No. 61372171 and the National Key Technology Research and Development Program of China under Grant No. 2012BAH23B03. Acknowledgement We thank anonymous reviewers for their constructive and valuable comments. We also thank Professor Jian-Feng Zhan at Institute of Computing Technology, Chinese Academy of Sciences, Beijing, for his technical suggestions on this paper.
文摘Learning structure from data is one of the most important fundamental tasks of Bayesian network research. Particularly, learning optional structure of Bayesian network is a non-deterministic polynomial-time （NP） hard problem. To solve this problem, many heuristic algorithms have been proposed, and some of them learn Bayesian network structure with the help of different types of prior knowledge. However, the existing algorithms have some restrictions on the prior knowledge, such as quality restriction and use restriction. This makes it di？cult to use the prior knowledge well in these algorithms. In this paper, we introduce the prior knowledge into the Markov chain Monte Carlo （MCMC） algorithm and propose an algorithm called Constrained MCMC （C-MCMC） algorithm to learn the structure of the Bayesian network. Three types of prior knowledge are defined： existence of parent node, absence of parent node, and distribution knowledge including the conditional probability distribution （CPD） of edges and the probability distribution （PD） of nodes. All of these types of prior knowledge are easily used in this algorithm. We conduct extensive experiments to demonstrate the feasibility and effectiveness of the proposed method C-MCMC.
基金supported by the National Key R&D Program of China(2018YFB1402600)the National Natural Science Foundation of China(Grant Nos.61802028,62192784,61877006,and 62002027)。
文摘Node classification has a wide range of application scenarios such as citation analysis and social network analysis.In many real-world attributed networks,a large portion of classes only contain limited labeled nodes.Most of the existing node classification methods cannot be used for few-shot node classification.To train the model effectively and improve the robustness and reliability of the model with scarce labeled samples,in this paper,we propose a local adaptive discriminant structure learning(LADSL)method for few-shot node classification.LADSL aims to properly represent the nodes in the attributed graphs and learn a metric space with a strong discriminating power by reducing the intra-class variations and enlargingginter-classdifferences.Extensiveexperiments conducted on various attributed networks datasets demonstrate that LADSL is superior to the other methods on few-shot node classification task.
文摘In this paper, we propose a more efficient Bayesian network structure learning algorithm under the framework of score based local learning （SLL）. Our algorithm significantly improves computational efficiency by restricting the neighbors of each variable to a small subset of candidates and storing necessary information to uncover the spouses, at the same time guaranteeing to find the optimal neighbor set in the same sense as SLL. The algorithm is the- oretically sound in the sense that it is optimal in the limit of large sample size. Empirical results testify its improved speed without loss of quality in the learned structures.
基金supported by the National Natural Science Foundation of China(61573285).
文摘How to improve the efficiency of exact learning of the Bayesian network structure is a challenging issue.In this paper,four different causal constraints algorithms are added into score calculations to prune possible parent sets,improving state-ofthe-art learning algorithms’efficiency.Experimental results indicate that exact learning algorithms can significantly improve the efficiency with only a slight loss of accuracy.Under causal constraints,these exact learning algorithms can prune about 70%possible parent sets and reduce about 60%running time while only losing no more than 2%accuracy on average.Additionally,with sufficient samples,exact learning algorithms with causal constraints can also obtain the optimal network.In general,adding max-min parents and children constraints has better results in terms of efficiency and accuracy among these four causal constraints algorithms.
基金supported by the Fundamental Research Funds for the Central Universities,the Science and Technology Commission of Shanghai Municipality(No.19511120601)the Scientific and Technological Innovation 2030 Major Projects(No.2018AAA0100902)+1 种基金the CCF-AFSG Research Fund(No.CCF-AFSG RF20220205)the“Chenguang Program”sponsored by Shanghai Education Development Foundation and Shanghai Municipal Education Commission(No.21CGA32).
文摘Bayesian network is a popular approach to uncertainty knowledge representation and reasoning. Structure learning is the first step to learn a Bayesian network. Score-based methods are one of the most popular ways of learning the structure. In most cases, the score of Bayesian network is defined as adding the log-likelihood score and complexity score by using the penalty function. If the penalty function is set unreasonably, it may hurt the performance of structure search. Thus, Bayesian network structure learning is essentially a bi-objective optimization problem. However, the existing bi-objective structure learning algorithms can only be applied to small-scale networks. To this end, this paper proposes a bi-objective evolutionary Bayesian network structure learning algorithm via skeleton constraint (BBS) for the medium-scale networks. To boost the performance of searching, BBS introduces the random order prior (ROP) initial operator. ROP generates a skeleton to constrain the searching space, which is the key to expanding the scale of structure learning problems. Then, the acyclic structures are guaranteed by adding the orders of variables in the initial skeleton. After that, BBS designs the Pareto rank based crossover and skeleton guided mutation operators. The operators operate on the skeleton obtained in ROP to make the search more targeted. Finally, BBS provides a strategy to choose the final solution. The experimental results show that BBS can always find the structure which is closer to the ground truth compared with the single-objective structure learning methods. Furthermore, compared with the existing bi-objective structure learning methods, BBS is scalable and can be applied to medium-scale Bayesian network datasets. On the educational problem of discovering the influencing factors of students’ academic performance, BBS provides higher quality solutions and is featured with the flexibility of solution selection compared with the widely-used Bayesian network structure learning methods.
基金The authors extended their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through the Large Groups Project under grant number RGP.2/132/43。
文摘At present Bayesian Networks(BN)are being used widely for demonstrating uncertain knowledge in many disciplines,including biology,computer science,risk analysis,service quality analysis,and business.But they suffer from the problem that when the nodes and edges increase,the structure learning difficulty increases and algorithms become inefficient.To solve this problem,heuristic optimization algorithms are used,which tend to find a near-optimal answer rather than an exact one,with particle swarm optimization(PSO)being one of them.PSO is a swarm intelligence-based algorithm having basic inspiration from flocks of birds(how they search for food).PSO is employed widely because it is easier to code,converges quickly,and can be parallelized easily.We use a recently proposed version of PSO called generalized particle swarm optimization(GEPSO)to learn bayesian network structure.We construct an initial directed acyclic graph(DAG)by using the max-min parent’s children(MMPC)algorithm and cross relative average entropy.ThisDAGis used to create a population for theGEPSO optimization procedure.Moreover,we propose a velocity update procedure to increase the efficiency of the algorithmic search process.Results of the experiments show that as the complexity of the dataset increases,our algorithm Bayesian network generalized particle swarm optimization(BN-GEPSO)outperforms the PSO algorithm in terms of the Bayesian information criterion(BIC)score.
基金Supported by the National Natural Science Foundation of China(61273160)the Fundamental Research Funds for the Central Universities(14CX06067A,13CX05021A)
文摘In soft sensor field, just-in-time learning(JITL) is an effective approach to model nonlinear and time varying processes. However, most similarity criterions in JITL are computed in the input space only while ignoring important output information, which may lead to inaccurate construction of relevant sample set. To solve this problem, we propose a novel supervised feature extraction method suitable for the regression problem called supervised local and non-local structure preserving projections(SLNSPP), in which both input and output information can be easily and effectively incorporated through a newly defined similarity index. The SLNSPP can not only retain the virtue of locality preserving projections but also prevent faraway points from nearing after projection,which endues SLNSPP with powerful discriminating ability. Such two good properties of SLNSPP are desirable for JITL as they are expected to enhance the accuracy of similar sample selection. Consequently, we present a SLNSPP-JITL framework for developing adaptive soft sensor, including a sparse learning strategy to limit the scale and update the frequency of database. Finally, two case studies are conducted with benchmark datasets to evaluate the performance of the proposed schemes. The results demonstrate the effectiveness of LNSPP and SLNSPP.
基金This project was supported by the National Natural Science Foundation of China (70572045).
文摘A new method to evaluate the fitness of the Bayesian networks according to the observed data is provided. The main advantage of this criterion is that it is suitable for both the complete and incomplete cases while the others not. Moreover it facilitates the computation greatly. In order to reduce the search space, the notation of equivalent class proposed by David Chickering is adopted. Instead of using the method directly, the novel criterion, variable ordering, and equivalent class are combined,moreover the proposed mthod avoids some problems caused by the previous one. Later, the genetic algorithm which allows global convergence, lack in the most of the methods searching for Bayesian network is applied to search for a good model in thisspace. To speed up the convergence, the genetic algorithm is combined with the greedy algorithm. Finally, the simulation shows the validity of the proposed approach.
基金supported by the National Natural Science Foundation of China (60974082,11171094)the Fundamental Research Funds for the Central Universities (K50510700004)+1 种基金the Foundation and Advanced Technology Research Program of Henan Province (102300410264)the Basic Research Program of the Education Department of Henan Province (2010A110010)
文摘Structure learning of Bayesian networks is a wellresearched but computationally hard task.For learning Bayesian networks,this paper proposes an improved algorithm based on unconstrained optimization and ant colony optimization（U-ACO-B） to solve the drawbacks of the ant colony optimization（ACO-B）.In this algorithm,firstly,an unconstrained optimization problem is solved to obtain an undirected skeleton,and then the ACO algorithm is used to orientate the edges,thus returning the final structure.In the experimental part of the paper,we compare the performance of the proposed algorithm with ACO-B algorithm.The experimental results show that our method is effective and greatly enhance convergence speed than ACO-B algorithm.
文摘We propose an approach for dependence tree structure learning via copula. A nonparametric algorithm for copula estimation is presented. Then a Chow-Liu like method based on dependence measure via copula is proposed to estimate maximum spanning bivariate copula associated with bivariate dependence relations. The main advantage of the approach is that learning with empirical copula focuses on dependence relations among random variables, without the need to know the properties of individual variables as well as without the requirement to specify parametric family of entire underlying distribution for individual variables. Experiments on two real-application data sets show the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China (No. 60974082)
文摘Learning Bayesian network structure is one of the most important branches in Bayesian network. The most popular graphical representative of a Bayesian network structure is an essential graph. This paper shows a combined algorithm according to the three rules for finding the essential graph of a given directed acyclic graph. Moreover, the complexity and advantages of this combined algorithm over others are also discussed. The aim of this paper is to present the proof of the correctness of the combined algorithm.
