基于节点块序列约束的局部贝叶斯网络结构搜索算法

王海羽; 刘浩然; 张力悦; 张春兰; 刘彬

doi:10.16383/j.aas.c180108

基于节点块序列约束的局部贝叶斯网络结构搜索算法

doi: 10.16383/j.aas.c180108

王海羽^{1, 2,},
刘浩然^{1, 2, ,},
张力悦^{1, 2,},
张春兰^{1, 2,},
刘彬^{1, 2,}

1.
燕山大学信息科学与工程学院秦皇岛 066004
2.
燕山大学河北省特种光纤与光纤传感重点实验室秦皇岛 066004

基金项目:

国家自然科学基金 51641609

国家自然科学基金 61802333

详细信息

作者简介:
王海羽  燕山大学信息科学与工程学院硕士研究生.主要研究方向为贝叶斯网络, 动态贝叶斯网络, 人工智能, 进化算法, 故障诊断与预测. E-mail: anderwwhy@outlook.com

张力悦  燕山大学信息科学与工程学院硕士研究生.主要研究方向为智能算法, 贝叶斯网络, 故障诊断与预测. E-mail: zly15128506765@163.com

张春兰  燕山大学信息科学与工程学院硕士研究生.主要研究方向为智能优化, 贝叶斯网络, 故障诊断与预测. E-mail: 15076053886@163.com

刘彬  燕山大学信息科学与工程学院教授.主要研究方向为深度学习, 贝叶斯网络, 故障诊断与预测. E-mail: liubin@ysu.edu.cn

通讯作者:
刘浩然燕山大学信息科学与工程学院教授.主要研究方向为贝叶斯网络, 人工智能, 无线传感器网络, 故障诊断与预测.本文通信作者. E-mail: liuhaoranysu125@163.com

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出版历程
- 收稿日期: 2018-02-27
- 录用日期: 2018-08-28
- 刊出日期: 2020-07-10

Local Bayesian Network Structure Searching Using Constraint of Node Chunk Sequence

WANG Hai-Yu^{1, 2
,},
LIU Hao-Ran^{1, 2
, ,},
ZHANG Li-Yue^{1, 2
,},
ZHANG Chun-Lan^{1, 2
,},
LIU Bin^{1, 2
,}

1.
School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004
2.
Key Laboratory for Special Fiber and Fiber Sensor of Hebei Province, Yanshan University, Qinhuangdao 066004

Funds:

National Natural Science Foundation of China 51641609

National Natural Science Foundation of China 61802333

More Information

Author Bio:
WANG Hai-Yu  Master student at the College of Information Science and Engineering, Yanshan University. His research interest covers Bayesian network, artiflcial intelligence, evolutionary computation, and fault diagnosis and prediction

ZHANG Li-Yue  Master student at the College of Information Science and Engineering, Yanshan University. His research interest covers intelligent algorithms, Bayesian networks, and fault diagnosis and prediction

ZHANG Chun-Lan  Master student at the College of Information Science and Engineering, Yanshan University. Her research interest covers intelligent optimization, Bayesian network, and fault diagnosis and prediction

LIU Bin  Professor at the College of Information Science and Engineering, Yanshan University. His research interest covers deep learning, Bayesian network, and fault diagnosis and prediction

Corresponding author: LIU Hao-Ran Professor at the College of Information Science and Engineering, Yanshan University. His research interest covers Bayesian network, artiflcial intelligence, wireless sensor networks, and fault diagnosis and prediction. Corresponding author of this paper

摘要

摘要: 针对K2算法过度依赖节点序和节点序搜索算法评价节点序效率较低的问题, 提出一种基于节点块序列约束的局部贝叶斯网络结构搜索算法, 该算法首先通过评分定向构建定向支撑树结构, 在此基础上构建节点块序列, 然后利用节点块序列确定每个节点的潜在父节点集, 通过搜索每个节点的父节点集构建网络结构, 最后对该结构进行非法结构修正得到最优贝叶斯网络结构.利用标准网络将算法与几种不同类型的改进算法进行对比分析, 验证该算法的有效性.
- 贝叶斯网络结构学习 /
- 定向最大支撑树 /
- 节点块序列 /
- K2算法
Abstract: The performance of the K2 algorithm depends on node ordering heavily. The Bayesian learning algorithm based on node order search needs to evaluate the quality of the node sequence by K2 algorithm, resulting in the problem of low efficiency in large and medium-sized networks. In this paper, a new Bayesian structure learning algorithm is proposed to solve the BN structure learning problem by searching local Bayesian network structure construction using node chunk sequence constraints. The algorithm firstly constructs a directional maximum weight spanning tree structure by using score orientation and generates the node chunk sequence by this structure. Then, the node chunk sequence is used to determine the potential parent node set of each node. The network structure is built by searching the parent node set of each node, and the structure is modified by illegal structure to get the optimal Bayesian network structure. Finally, some experiments are designed to evaluate the performance of the proposed algorithm, in which the standard network is used to compare the algorithm with several different improved algorithms to verify the effectiveness of the algorithm. The results indicate that the proposed algorithm is worthy of being studied in the field of BNs construction.
- Bayesian network structure learning /
- directional maximum weight spanning tree /
- the node chunk sequence /
- K2 algorithm
Recommended by Associate Editor LI Ming
注释:

1) 本文责任编委黎铭

HTML全文

图 1 由定向支撑树构建节点块序列的例子

Fig. 1 Example of constructing node chunk sequence by directional support tree

下载: 全尺寸图片幻灯片

图 2 由节点块序列搜索潜在父节点集的简单例子

Fig. 2 A simple example of searching potential parent set by node chunk sequence

下载: 全尺寸图片幻灯片

图 3 Alarm网络中不同算法精度对比

Fig. 3 Comparison of different algorithm accuracy in Alarm network

下载: 全尺寸图片幻灯片

图 4 Insurance网络中不同算法精度对比

Fig. 4 Comparison of different algorithm accuracy in Insurance network

下载: 全尺寸图片幻灯片

图 5 Hailfinder网络中不同算法精度对比

Fig. 5 Comparison of different algorithm accuracy in Hailfinder network

下载: 全尺寸图片幻灯片

表 1 标准贝叶斯网络的参数

Table 1 Parameters of standard Bayesian networks

网络	节点数	边数	变量域	最大节点出入度
Alarm	37	46	2~4	6
Insurance	27	52	2~5	9
Hailfinder	56	66	2~11	17

下载: 导出CSV

表 2 标准贝叶斯网络结构平均BIC得分

Table 2 Average BIC score in standard Bayesian network structure

网络	1 000	2 000	3 000	5 000
Alarm	-10 874.35	-20 382.51	-30 057.28	-48 056.66
Insurance	-15 998.20	-30 103.21	-43 863.15	-73 069.35
Hailfinder	-67 046.62	-126 837.31	-176 348.73	-279 766.12

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表 3 NCSC算法与标准节点序的K2算法在Alarm网络中运行结果

Table 3 Results of NCSC algorithm and standard node sequence K2 algorithm in Alarm network

Alarm		BIC	Ext (s)	结构
Alarm		BIC	Ext (s)	C	M	R	A	W
1 000	NCSC	-11 410.83	32.98±1.82	41.8	2.1	2.8	6.5	11.4
1 000	K2	-11 189.51	10.27±0.61	44.2	1.8	0	4.3	6.1
2 000	NCSC	-20 791.86	42.14±1.88	41.7	1.9	2.2	6.2	10.3
2 000	K2	-20 605.99	11.53±0.47	44.5	1.5	0	2.7	4.2
3 000	NCSC	-31 025.28	45.99±5.93	42.9	1.3	2.2	4.2	7.7
3 000	K2	-30 505.01	14.04±1.95	44.9	1.1	0	3.1	4.2
5 000	NCSC	-49 812.61	56.25±2.13	43.2	1.2	1.1	4.7	7
5 000	K2	-49 235.77	16.51±0.74	45.1	1.0	0.0	3.1	4.1

下载: 导出CSV

表 4 NCSC算法与标准节点序的K2算法在Insurance网络中运行结果

Table 4 Results of NCSC algorithm and standard node sequence K2 algorithm in Insurance network

Insurance		BIC	Ext (s)	结构
Insurance		BIC	Ext (s)	C	M	R	A	W
1 000	NCSC	-16 486.31	17.28±0.34	38.3	11.9	2.3	2.6	16.8
1 000	K2	-16 219.71	4.58±0.25	39.7	12.3	0	0.3	12.6
2 000	NCSC	-30 756.3	19.61±1.13	39.1	10.7	2.4	3.2	16.3
2 000	K2	-30 544.86	5.11±0.31	42.2	9.8	0	0.5	10.3
3 000	NCSC	-45 369.23	24.34±3.22	39.8	10.2	2.3	3.3	15.8
3 000	K2	-44 748.8	6.32±0.40	42.6	9.4	0	0.5	9.9
5 000	NCSC	-73 566.77	29.92±2.91	40.6	9.4	2.3	3.2	14.9
5 000	K2	-73 148.28	7.68±0.45	43.8	8.2	0	0.6	8.8

下载: 导出CSV

表 5 NCSC算法与标准节点序的K2算法在Hailfinder网络中运行结果

Table 5 Results of NCSC algorithm and standard node sequence K2 algorithm in Hailfinder network

Insurance		BIC	Ext (s)	结构
Insurance		BIC	Ext (s)	C	M	R	A	W
1 000	NCSC	-78 396.62	232.18±16.31	47.8	16.3	2.8	9.7	29.3
1 000	K2	-78 157.99	25.71±1.55	48.3	17.7	0	8.1	25.8
2 000	NCSC	-131 604.2	250.58±7.94	50.2	13.9	1.6	10.1	25.6
2 000	K2	-130 945.5	30.22±1.51	51.6	14.4	0	9.1	23.5
3 000	NCSC	-182 167.2	292.22±20.01	51.5	13.4	1.4	10.3	25.1
3 000	K2	-181 831.9	36.58±1.84	52.9	13.1	0	9.5	22.6
5 000	NCSC	-283 288.4	356.14±16.77	51.8	12.8	1.8	10.1	24.7
5 000	K2	-282 937.2	43.37±1.83	53.5	12.5	0	9.9	22.4

下载: 导出CSV

表 6 五种算法在Alarm网络中运行时间(s)

Table 6 Running time of five algorithms in Alarm network (s)

Alarm	1 000	2 000	3 000	5 000
NCSC	32.98±1.82	42.14±1.88	45.99±2.04	56.25±2.13
K2+T	11.72±0.74	14.82±1.62	16.33±1.25	18.82±2.71
MAK	942.60±31.4	1 153.37±32.37	1 299.01±42.55	1 582.35±46.86
SHC	3 474.01±90.80	4 079.66±121.98	4 784.10±156.85	6 013.93±216.64
SAR	46.77±0.81	49.64±3.52	62.30±3.38	77.39±10.91

下载: 导出CSV

表 7 五种算法在Insurance网络中运行时间

Table 7 Running time of five algorithms in Insurance network (s)

Insurance	1 000	2 000	3 000	5 000
NCSC	17.28±0.34	19.61±1.13	24.34±3.22	29.92±2.91
K2+T	4.55±0.41	6.03±1.20	7.17±0.83	9.42±2.59
MAK	388.99±12.41	420.61±27.73	481.50±32.86	694.92±30.30
SHC	4 051.46±123.82	5 521.37±179.04	5 701.31±207.10	7 072.01±241.25
SAR	19.38±0.90	19.95±1.55	31.67±4.81	40.60±5.95

下载: 导出CSV

表 8 五种算法在Hailfinder网络中运行时间(s)

Table 8 Running time of five algorithms in Hailfinder network (s)

Hailflnder	1 000	2 000	3 000	5 000
NCSC	232.18±6.31	250.58±7.94	292.22±10.73	356.14±14.86
K2+T	28.54±0.92	32.82±0.93	39.21±1.16	49.38±1.76
MAK	2 203.76±61.58	2 611.30±66.94	3 100.82±96.87	3 854.99±120.45
SHC	18 273.69±468.55	23 500.71±318.11	29 255.29±380.52	35 785.38±420.00
SAR	229.07±7.82	264.35±15.53	307.52±12.35	362.27±20.55

下载: 导出CSV

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基于节点块序列约束的局部贝叶斯网络结构搜索算法

doi: 10.16383/j.aas.c180108

通讯作者:
刘浩然燕山大学信息科学与工程学院教授.主要研究方向为贝叶斯网络, 人工智能, 无线传感器网络, 故障诊断与预测.本文通信作者. E-mail: liuhaoranysu125@163.com

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Local Bayesian Network Structure Searching Using Constraint of Node Chunk Sequence

Corresponding author: LIU Hao-Ran Professor at the College of Information Science and Engineering, Yanshan University. His research interest covers Bayesian network, artiflcial intelligence, wireless sensor networks, and fault diagnosis and prediction. Corresponding author of this paper

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基于节点块序列约束的局部贝叶斯网络结构搜索算法

doi: 10.16383/j.aas.c180108

通讯作者: 刘浩然 燕山大学信息科学与工程学院教授.主要研究方向为贝叶斯网络, 人工智能, 无线传感器网络, 故障诊断与预测.本文通信作者. E-mail: liuhaoranysu125@163.com

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Local Bayesian Network Structure Searching Using Constraint of Node Chunk Sequence

Corresponding author: LIU Hao-Ran Professor at the College of Information Science and Engineering, Yanshan University. His research interest covers Bayesian network, artiflcial intelligence, wireless sensor networks, and fault diagnosis and prediction. Corresponding author of this paper

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通讯作者:
刘浩然燕山大学信息科学与工程学院教授.主要研究方向为贝叶斯网络, 人工智能, 无线传感器网络, 故障诊断与预测.本文通信作者. E-mail: liuhaoranysu125@163.com