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
Frequent counting is a very so often required operation in machine learning algorithms. A typical machine learning task, learning the structure of Bayesian network （BN） based on metric scoring, is introduced as an e...Frequent counting is a very so often required operation in machine learning algorithms. A typical machine learning task, learning the structure of Bayesian network （BN） based on metric scoring, is introduced as an example that heavily relies on frequent counting. A fast calculation method for frequent counting enhanced with two cache layers is then presented for learning BN. The main contribution of our approach is to eliminate comparison operations for frequent counting by introducing a multi-radix number system calculation. Both mathematical analysis and empirical comparison between our method and state-of-the-art solution are conducted. The results show that our method is dominantly superior to state-of-the-art solution in solving the problem of learning BN.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
Learning Bayesian network structure is one of the most exciting challenges in machine learning. Discovering a correct skeleton of a directed acyclic graph（DAG） is the foundation for dependency analysis algorithms fo...Learning Bayesian network structure is one of the most exciting challenges in machine learning. Discovering a correct skeleton of a directed acyclic graph（DAG） is the foundation for dependency analysis algorithms for this problem. Considering the unreliability of high order condition independence（CI） tests, and to improve the efficiency of a dependency analysis algorithm, the key steps are to use few numbers of CI tests and reduce the sizes of conditioning sets as much as possible. Based on these reasons and inspired by the algorithm PC, we present an algorithm, named fast and efficient PC（FEPC）, for learning the adjacent neighbourhood of every variable. FEPC implements the CI tests by three kinds of orders, which reduces the high order CI tests significantly. Compared with current algorithm proposals, the experiment results show that FEPC has better accuracy with fewer numbers of condition independence tests and smaller size of conditioning sets. The highest reduction percentage of CI test is 83.3% by EFPC compared with PC algorithm.展开更多
Breast cancer is the leading cause of cancer-related death for women in Tunisia and the prognosis of its metastasis remains a major problem for oncologists despite advances in treatment. In this work we use Bayesian n...Breast cancer is the leading cause of cancer-related death for women in Tunisia and the prognosis of its metastasis remains a major problem for oncologists despite advances in treatment. In this work we use Bayesian networks to develop a decision support system that is based on the modeling of relationships between key signaling proteins and clinical and pathological characteristics of breast tumors and patients. Motivated by the lack of prior information on the parameters of the problem, we use the Implicit inference for the structure and parameter learning. A dataset of 84 Tunisian breast cancer patients was used and new prognosis factors were identified. The system predicts a metastasis risk for different patients by computing a score that is the joint probability of the Bayesian network using parameters estimated on the learning database. Based on the results of the developed system we identified that overexpression of ErbB2, ErbB3, bcl2 as well as of oestrogen and progesterone receptors associated with a low level of ErbB4 was the predominant profile associated with high risk of metastasis.展开更多
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.
基金supported by National Natural Science Foundation of China (No.60970055)
文摘Frequent counting is a very so often required operation in machine learning algorithms. A typical machine learning task, learning the structure of Bayesian network （BN） based on metric scoring, is introduced as an example that heavily relies on frequent counting. A fast calculation method for frequent counting enhanced with two cache layers is then presented for learning BN. The main contribution of our approach is to eliminate comparison operations for frequent counting by introducing a multi-radix number system calculation. Both mathematical analysis and empirical comparison between our method and state-of-the-art solution are conducted. The results show that our method is dominantly superior to state-of-the-art solution in solving the problem of learning BN.
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(61403290,11301408,11401454)the Foundation for Youths of Shaanxi Province(2014JQ1020)+1 种基金the Foundation of Baoji City(2013R7-3)the Foundation of Baoji University of Arts and Sciences(ZK15081)
文摘Learning Bayesian network structure is one of the most exciting challenges in machine learning. Discovering a correct skeleton of a directed acyclic graph（DAG） is the foundation for dependency analysis algorithms for this problem. Considering the unreliability of high order condition independence（CI） tests, and to improve the efficiency of a dependency analysis algorithm, the key steps are to use few numbers of CI tests and reduce the sizes of conditioning sets as much as possible. Based on these reasons and inspired by the algorithm PC, we present an algorithm, named fast and efficient PC（FEPC）, for learning the adjacent neighbourhood of every variable. FEPC implements the CI tests by three kinds of orders, which reduces the high order CI tests significantly. Compared with current algorithm proposals, the experiment results show that FEPC has better accuracy with fewer numbers of condition independence tests and smaller size of conditioning sets. The highest reduction percentage of CI test is 83.3% by EFPC compared with PC algorithm.
文摘Breast cancer is the leading cause of cancer-related death for women in Tunisia and the prognosis of its metastasis remains a major problem for oncologists despite advances in treatment. In this work we use Bayesian networks to develop a decision support system that is based on the modeling of relationships between key signaling proteins and clinical and pathological characteristics of breast tumors and patients. Motivated by the lack of prior information on the parameters of the problem, we use the Implicit inference for the structure and parameter learning. A dataset of 84 Tunisian breast cancer patients was used and new prognosis factors were identified. The system predicts a metastasis risk for different patients by computing a score that is the joint probability of the Bayesian network using parameters estimated on the learning database. Based on the results of the developed system we identified that overexpression of ErbB2, ErbB3, bcl2 as well as of oestrogen and progesterone receptors associated with a low level of ErbB4 was the predominant profile associated with high risk of metastasis.
