面向智慧教育的知识追踪模型研究综述

doi:10.3778/j.issn.1673-9418.2111054

计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (8): 1742-1763.DOI: 10.3778/j.issn.1673-9418.2111054

面向智慧教育的知识追踪模型研究综述

曾凡智, 许露倩(), 周燕, 周月霞, 廖俊玮

佛山科学技术学院计算机系，广东佛山 528000

收稿日期:2021-11-10 修回日期:2022-03-24 出版日期:2022-08-01 发布日期:2022-08-19
通讯作者: +E-mail: xuluqian1002@163.com.
作者简介:曾凡智（1965—），男，湖北洪湖人，博士，教授，硕士生导师，CCF会员，主要研究方向为计算机视觉、图像处理、数据挖掘。
许露倩（1995—），女，河南南阳人，硕士研究生，主要研究方向为计算机视觉、数据挖掘。
周燕（1979—），女，江西抚州人，硕士，教授，硕士生导师，CCF会员，主要研究方向为计算机视觉、压缩感知、三维模型检索。
周月霞（1978—），女，湖北监利人，硕士，讲师，主要研究方向为信息采集与处理。
廖俊玮（1996—），男，广东梅州人，硕士研究生，主要研究方向为计算机视觉、场景文字检测与识别。
基金资助:
国家自然科学基金(61972091);广东省自然科学基金(2022A1515010101);广东省自然科学基金(2021A1515012639);广东省普通高校重点研究项目(2019KZDXM007);广东省普通高校重点研究项目(2020ZDZX3049);佛山市科技创新项目(2020001003285)

Review of Knowledge Tracing Model for Intelligent Education

ZENG Fanzhi, XU Luqian(), ZHOU Yan, ZHOU Yuexia, LIAO Junwei

Department of Computer Science, Foshan University, Foshan, Guangdong 528000, China

Received:2021-11-10 Revised:2022-03-24 Online:2022-08-01 Published:2022-08-19
About author:ZENG Fanzhi, born in 1965, Ph.D., professor, M.S. supervisor, member of CCF. His research interests include computer vision, image processing and data mining.
XU Luqian, born in 1995, M.S. candidate. Her research interests include computer vision and data mining.
ZHOU Yan, born in 1979, M.S., professor, M.S. supervisor, member of CCF. Her research interests include computer vision, compressive sensing and 3D model retrieval.
ZHOU Yuexia, born in 1978, M.S., lecturer. Her research interests include information acquisition and processing.
LIAO Junwei, born in 1996, M.S. candidate. His research interests include computer vision, scene text detection and recognition.
Supported by:
the National Natural Science Foundation of China(61972091);the Natural Science Foundation of Guangdong Province(2022A1515010101);the Natural Science Foundation of Guangdong Province(2021A1515012639);the Key Research Project of University of Guangdong Province(2019KZDXM007);the Key Research Project of University of Guangdong Province(2020ZDZX3049);the Science and Technology Innovation Project of Foshan(2020001003285)

摘要/Abstract

摘要：

知识追踪（KT）作为智慧教育领域的重点研究方向之一，利用智能辅导系统（ITS）提供的大量学习轨迹信息对学生进行建模，自动衡量学生的知识水平，为其提供个性化的学习方案，达到人工智能辅助教育的目的。全面回顾了面向智慧教育的知识追踪模型研究进展，三类具有代表性的模型分别为基于贝叶斯的知识追踪、基于Logistic模型的知识追踪以及近年来迅速发展并且表现出更好性能的深度学习知识追踪。基于贝叶斯的知识追踪分为贝叶斯知识追踪（BKT）以及结合个性化、知识相关性、节点状态与现实问题扩展的BKT模型;基于Logistic模型的知识追踪分为项目反应理论（IRT）与因子分析模型两类;基于深度学习的知识追踪分为深度知识追踪（DKT）及其改进模型以及设计网络结构与引入注意力机制。介绍了目前可供研究者们使用的国际公开教育数据集与常用的模型评估指标，比较和分析了不同类型方法的性能、特点以及应用场景，并对当前研究所存在的问题以及未来发展方向进行探讨与展望。

关键词: 知识追踪（KT）, 智慧教育, 贝叶斯网络, Logistic模型, 深度学习

Abstract:

As one of the key research directions in the field of intelligent education, knowledge tracing (KT) makes use of a large amount of learning trajectory information provided by the intelligent tutoring system (ITS) to model students, measure their knowledge level automatically, and provide personalized learning programs for them, to achieve the purpose of AI-assisted education. The research progress of knowledge tracing models for intelligent education is reviewed comprehensively. Three representative models are knowledge tracing based on Bayes, knowledge tracing based on Logistic regression model, and deep learning knowledge tracing which has developed rapidly in recent years and shows better performance. Knowledge tracing based on Bayes is divided into Bayesian knowledge tracing (BKT) and BKT model combining personalization, knowledge correlation, node state and real problem expansion. Knowledge tracing based on Logistic regression model is divided into item response theory (IRT) and factor analysis model. Knowledge tracing based on deep learning can be divided into deep knowledge tracing (DTK) and its improved model, designing network structure and introducing attention mechanism. The international open education datasets available to researchers and the commonly used model evaluation indicators are introduced. The performance, characteristics and application scenarios of different types of methods are compared and analyzed. It also discusses the existing problems of the current research and looks forward to future develop-ment direction.

Key words: knowledge tracing (KT), intelligent education, Bayesian network, Logistic regression, deep learning

中图分类号:

TP391

曾凡智, 许露倩, 周燕, 周月霞, 廖俊玮. 面向智慧教育的知识追踪模型研究综述[J]. 计算机科学与探索, 2022, 16(8): 1742-1763.

ZENG Fanzhi, XU Luqian, ZHOU Yan, ZHOU Yuexia, LIAO Junwei. Review of Knowledge Tracing Model for Intelligent Education[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(8): 1742-1763.

图/表 22

图1 基于贝叶斯方法脉络图

Fig.1 Venation diagram of Bayesian method

图2 BKT模型结构

Fig.2 Architecture of BKT

表1 BKT模型扩展方法概览

Table 1 Overview of BKT model extension methods

研究	发表年份	扩展类别	方法概述	局限性
Pardos等人^[12]	2010	结合个性化	为每个学生设计不同初始背景的知识状态	依赖于简化的假设，如每道题目仅涉及一个KC，学习过程中不存在遗忘情况等
Lee等人^[13]	2012	结合个性化	设计学生导向模型，提高个体性差异
Yudelson等人^[14]	2013	结合个性化	将模型参数划分为知识部分和学生部分提高模型性能
Wang等人^[15]	2020	结合个性化	基于聚类学生进行贝叶斯知识追踪
Käser等人^[16]	2014	结合知识相关性	使用DBN表示KC拓扑结构	需要设置阈值，而不同类型KC需要不一样的阈值范围以及设置依据
Hawkins等人^[17]	2014	结合知识相关性	考虑到题目相似性的BKT-ST模型
Wang等人^[18]	2016	结合知识相关性	基于知识状态的层次性和时间特性进行建模
Käser等人^[19]	2017	结合知识相关性	利用DBK在单个模型中联合考虑不同的KC
Wang等人^[21]	2013	结合节点状态	采用0到1的连续型表示法，细化学生的知识状态	参数较多，计算量大，复杂度高
Falakmasir等人^[20]	2015	结合节点状态	用3-gram代替二元节点状态的Spectral BKT模型
Zhang等人^[22]	2018	结合节点状态	采用三支决策的思想改进二进制节点状态
Pardos等人^[24]	2011	结合现实问题	将题目的难度系数引入BKT	先验概率的确定存在主观性，简单的模型很难纳入实际情况的复杂性
Xu等人^[25]	2014	结合现实问题	利用脑电图探测学生做题时的心理
Spaulding等人^[26]	2015	结合现实问题	融入学生的情感状态
Agarwal等人^[28]	2020	结合现实问题	引入学生答题情况近期率权重的MS-BKT模型，细化学生知识状态
黄诗雯等人^[27]	2021	结合现实问题	融合了学生的学习行为与遗忘因素

表1 BKT模型扩展方法概览

Table 1 Overview of BKT model extension methods

研究	发表年份	扩展类别	方法概述	局限性
Pardos等人^[12]	2010	结合个性化	为每个学生设计不同初始背景的知识状态	依赖于简化的假设，如每道题目仅涉及一个KC，学习过程中不存在遗忘情况等
Lee等人^[13]	2012	结合个性化	设计学生导向模型，提高个体性差异
Yudelson等人^[14]	2013	结合个性化	将模型参数划分为知识部分和学生部分提高模型性能
Wang等人^[15]	2020	结合个性化	基于聚类学生进行贝叶斯知识追踪
Käser等人^[16]	2014	结合知识相关性	使用DBN表示KC拓扑结构	需要设置阈值，而不同类型KC需要不一样的阈值范围以及设置依据
Hawkins等人^[17]	2014	结合知识相关性	考虑到题目相似性的BKT-ST模型
Wang等人^[18]	2016	结合知识相关性	基于知识状态的层次性和时间特性进行建模
Käser等人^[19]	2017	结合知识相关性	利用DBK在单个模型中联合考虑不同的KC
Wang等人^[21]	2013	结合节点状态	采用0到1的连续型表示法，细化学生的知识状态	参数较多，计算量大，复杂度高
Falakmasir等人^[20]	2015	结合节点状态	用3-gram代替二元节点状态的Spectral BKT模型
Zhang等人^[22]	2018	结合节点状态	采用三支决策的思想改进二进制节点状态
Pardos等人^[24]	2011	结合现实问题	将题目的难度系数引入BKT	先验概率的确定存在主观性，简单的模型很难纳入实际情况的复杂性
Xu等人^[25]	2014	结合现实问题	利用脑电图探测学生做题时的心理
Spaulding等人^[26]	2015	结合现实问题	融入学生的情感状态
Agarwal等人^[28]	2020	结合现实问题	引入学生答题情况近期率权重的MS-BKT模型，细化学生知识状态
黄诗雯等人^[27]	2021	结合现实问题	融合了学生的学习行为与遗忘因素

图3 基于Logistic回归方法脉络图

Fig.3 Venation diagram of Logistic regression method

表2 基于Logistic模型方法对比

Table 2 Comparison of Logistic regression model

模型	发表年份	方法概述	局限性
LFA^[31]	2006	源于学习曲线的一种半自动化的方法	对练习时间具有敏感性
PFA^[32]	2009	LFA的改进方法，考虑题目的正误反应数量的学习累积	不能处理知识点之间的内在依赖性
IRT^[30]	2018	基于IRT理论，为学生能力和题目难度建立参数模型	学生的能力水平在学习过程中是固定的
KTM^[33]	2019	利用FMs将传统的Logistic模型推广到更高的维度	冷启动问题，不能准确代表之前的学习序列
RKTM^[35]	2021	引入学生知识状态，与当前学习场景交互	特征提取困难，参数较多，增加了学习复杂度

图4 基于深度学习方法脉络图

Fig.4 Venation diagram of deep learning method

图5 DKT模型结构

Fig.5 Architecture of DKT

图6 DKT+HFE模型结构

Fig.6 Architecture of DKT+HFE

图7 DKT+FB模型结构

Fig.7 Architecture of DKT+FB

图8 与遗忘相关的附加信息

Fig.8 Additional information related to forgetting

图9 DynEmb模型结构

Fig.9 Architecture of DynEmb

图10 DKVMN模型结构

Fig.10 Architecture of DKVMN

图11 CKT模型结构

Fig.11 Architecture of CKT

图12 t = 2与 t = 3时刻的向量说明

Fig.12 Vector description at t = 2 and t = 3

图13 DNC模型结构

Fig.13 Architecture of DNC

图14 练习 e i的文本嵌入

Fig.14 Exercise embedding for exercise e i

图15 SAINT模型结构

Fig.15 Architecture of SAINT

表3 深度学习方法对比

Table 3 Comparison of deep learning methods

模型	发表年份	类别	方法概述	局限性
DKT^[41]	2015	—	采用RNN或LSTM建模学生序列	—
Deep-IRT^[64]	2019	可解释性	结合心理测量理论IRT增强可解释性	模型参数较多，复杂度高，且每个参数也不具备传统方法的语义含义
KQN^[73]	2019	可解释性	利用向量化表示提高模型的直观性与可解释性
AKT^[88]	2020	可解释性	与一系列可解释的心理测量模型组件相结合
TC-MIRT^[49]	2021	可解释性	结合MIRT构建增强网络组件生成可解释的参数
DKT+^[50]	2018	融合学习特征	引入对应DKT模型的重构以及三个正则化项，增强预测的一致性	将各类异构特征整合到数据中存在一定难度，参数量过大，需要加大计算量，模型训练速度低，训练周期过长
DKT+HFE^[52]	2018	融合学习特征	应用树的分类器将异构特征隐式有效地嵌入DKT
DKT-DSC^[53]	2018	融合学习特征	定期将学生按能力动态分组，隐式嵌入学生特征
PDKT-C^[54]	2018	融合学习特征	结合题目信息的先决条件进行建模作为约束
DHKT^[55]	2019	融合学习特征	建模题目和KC之间的层次结构
DKT+FB^[56]	2019	融合学习特征	融合三点与遗忘相关的附加信息
DynEmb^[58]	2020	融合学习特征	将矩阵分解技术与RNN相结合
DKT LSTM^[57]	2021	融合学习特征	融合学生异构特征与遗忘行为相关信息，通过SAEN进行建模
LANA^[59]	2021	融合学习特征	通过一种新颖的SRFE从学生各自的交互序列中提取其内在属性
DKVMN^[61]	2017	动态键值记忆网络	借鉴MANN，利用静态、动态外部矩阵分别读写学生知识状态	网络模型较大，知识增长的计算有一定局限性，捕捉序列之间的依赖关系能力有限
DKVMN-CA^[63]	2019	动态键值记忆网络	改进DKVMN，支持人工标注概念树
LPKT^[65]	2020	动态键值记忆网络	采用DKVMN，结合学生的知识现状，完善模型的遗忘机制
DKVMN-LA^[66]	2021	动态键值记忆网络	引入学生学习能力与行为特征的多功能知识追踪算法
CKT^[72]	2020	3D卷积网络	采用3D ConvNets强化学生近期的学习状态与练习的短期特征	依赖特征工程提取，难以为高维数据提供准确的预测结果
GKT^[77]	2019	图神经网络	利用GNN构建KC关系图	计算密集型，易受数据集大小的限制，由于KC划分粒度不一致，可能会直接影响学生知识状态的评估性能
GIKT^[79]	2020	图神经网络	利用GCN提取练习-KC关系图中包含的高阶关系信息
HGKT^[81]	2020	图神经网络	结合练习之间的层次关系，建模练习学习依赖性
JKT^[80]	2021	图神经网络	联合图卷积网络提取隐藏在“练习-KC”图中的深层隐式信息
DGMN^[82]	2021	图神经网络	利用外部记忆结构的知识状态动态构建潜在KC及其关系图，同时考虑遗忘行为
HMN^[74]	2021	层次记忆网络	基于ASMM与DNC建模KT中的学生记忆机制	外部存储矩阵对记忆的划分不一，可能直接影响预测的准确度
EERNNA^[83]	2018	注意力机制	嵌入练习文本特征建模学生的学习过程	抑制了注意力机制周围的其他信息，没有考虑到练习的顺序
SAKT^[86]	2019	注意力机制	基于自注意力机制建模学生的交互历史，减少无关练习对目标练习的影响
SAINT^[87]	2020	注意力机制	改进SAKT，基于深度自注意层建模练习和学生回答之间的关系
AKT^[88]	2020	注意力机制	建模题目与回答的上下文感知，表示提取学生的猜测与失误特征
RKT^[89]	2020	注意力机制	利用上下文信息来增强自注意力机制，采用对指数衰减核函数建模学生遗忘行为
EKTA^[85]	2021	注意力机制	改进EERNNA，追踪学生对特定KC的掌握程度
MF-DAKT^[90]	2021	注意力机制	DAKT从不同角度捕捉因子和因子相互作用中包含的信息
ATKT^[91]	2021	注意力机制	利用高效注意力-LSTM自适应聚合先前知识隐藏状态的信息，通过AK增强模型的泛化能力

表3 深度学习方法对比

Table 3 Comparison of deep learning methods

模型	发表年份	类别	方法概述	局限性
DKT^[41]	2015	—	采用RNN或LSTM建模学生序列	—
Deep-IRT^[64]	2019	可解释性	结合心理测量理论IRT增强可解释性	模型参数较多，复杂度高，且每个参数也不具备传统方法的语义含义
KQN^[73]	2019	可解释性	利用向量化表示提高模型的直观性与可解释性
AKT^[88]	2020	可解释性	与一系列可解释的心理测量模型组件相结合
TC-MIRT^[49]	2021	可解释性	结合MIRT构建增强网络组件生成可解释的参数
DKT+^[50]	2018	融合学习特征	引入对应DKT模型的重构以及三个正则化项，增强预测的一致性	将各类异构特征整合到数据中存在一定难度，参数量过大，需要加大计算量，模型训练速度低，训练周期过长
DKT+HFE^[52]	2018	融合学习特征	应用树的分类器将异构特征隐式有效地嵌入DKT
DKT-DSC^[53]	2018	融合学习特征	定期将学生按能力动态分组，隐式嵌入学生特征
PDKT-C^[54]	2018	融合学习特征	结合题目信息的先决条件进行建模作为约束
DHKT^[55]	2019	融合学习特征	建模题目和KC之间的层次结构
DKT+FB^[56]	2019	融合学习特征	融合三点与遗忘相关的附加信息
DynEmb^[58]	2020	融合学习特征	将矩阵分解技术与RNN相结合
DKT LSTM^[57]	2021	融合学习特征	融合学生异构特征与遗忘行为相关信息，通过SAEN进行建模
LANA^[59]	2021	融合学习特征	通过一种新颖的SRFE从学生各自的交互序列中提取其内在属性
DKVMN^[61]	2017	动态键值记忆网络	借鉴MANN，利用静态、动态外部矩阵分别读写学生知识状态	网络模型较大，知识增长的计算有一定局限性，捕捉序列之间的依赖关系能力有限
DKVMN-CA^[63]	2019	动态键值记忆网络	改进DKVMN，支持人工标注概念树
LPKT^[65]	2020	动态键值记忆网络	采用DKVMN，结合学生的知识现状，完善模型的遗忘机制
DKVMN-LA^[66]	2021	动态键值记忆网络	引入学生学习能力与行为特征的多功能知识追踪算法
CKT^[72]	2020	3D卷积网络	采用3D ConvNets强化学生近期的学习状态与练习的短期特征	依赖特征工程提取，难以为高维数据提供准确的预测结果
GKT^[77]	2019	图神经网络	利用GNN构建KC关系图	计算密集型，易受数据集大小的限制，由于KC划分粒度不一致，可能会直接影响学生知识状态的评估性能
GIKT^[79]	2020	图神经网络	利用GCN提取练习-KC关系图中包含的高阶关系信息
HGKT^[81]	2020	图神经网络	结合练习之间的层次关系，建模练习学习依赖性
JKT^[80]	2021	图神经网络	联合图卷积网络提取隐藏在“练习-KC”图中的深层隐式信息
DGMN^[82]	2021	图神经网络	利用外部记忆结构的知识状态动态构建潜在KC及其关系图，同时考虑遗忘行为
HMN^[74]	2021	层次记忆网络	基于ASMM与DNC建模KT中的学生记忆机制	外部存储矩阵对记忆的划分不一，可能直接影响预测的准确度
EERNNA^[83]	2018	注意力机制	嵌入练习文本特征建模学生的学习过程	抑制了注意力机制周围的其他信息，没有考虑到练习的顺序
SAKT^[86]	2019	注意力机制	基于自注意力机制建模学生的交互历史，减少无关练习对目标练习的影响
SAINT^[87]	2020	注意力机制	改进SAKT，基于深度自注意层建模练习和学生回答之间的关系
AKT^[88]	2020	注意力机制	建模题目与回答的上下文感知，表示提取学生的猜测与失误特征
RKT^[89]	2020	注意力机制	利用上下文信息来增强自注意力机制，采用对指数衰减核函数建模学生遗忘行为
EKTA^[85]	2021	注意力机制	改进EERNNA，追踪学生对特定KC的掌握程度
MF-DAKT^[90]	2021	注意力机制	DAKT从不同角度捕捉因子和因子相互作用中包含的信息
ATKT^[91]	2021	注意力机制	利用高效注意力-LSTM自适应聚合先前知识隐藏状态的信息，通过AK增强模型的泛化能力

表4 公开数据集统计及其下载链接

Table 4 Public dataset statistics and download links

Datasets	Students	Concepts	Records	Website
ASSISTments2009	4 417	124	325 637	https://sites.google.com/site/assistmentsdata/home/assistment-2009-2010data/skill-builder-data-2009-2010
ASSISTments2012	27 405	265	2 541 201	https://sites.google.com/site/assistmentsdata/home/2012-13-school-data-with-affect
ASSISTments2015	19 917	100	683 801	https://sites.google.com/site/assistmentsdata/home/2015-assistments-skill-builderdata
ASSISTments2017	1 709	102	942 816	https://sites.google.com/view/assistmentsdatamining/dataset?authuser=0
KDD Cup2010	574	436	607 026	https://pslcdatashop.web.cmu.edu/KDDCup/downloads.jsp
Statics2011	335	1 362	361 092	https://pslcdatashop.web.cmu.edu/DatasetInfo?datasetId=507
Synthetic-5	4 000	50	200 000	https://github.com/chrispiech/DeepKnowledgeTracing/tree/master/data/synthetic
slepemapy.cz	91 331	1 459	10 087 306	https://www.fi.muni.cz/adaptivelearning/?a=data
EdNet	784 309	293	131 441 538	https://github.com/riiid/ednet
Junyi Academy	238 120	722	26 666 117	https://pslcdatashop.web.cmu.edu/DatasetInfo?datasetId=1198

表5 常用的评估指标

Table 5 Commonly used evaluation indicators

Specific metric	Formula mode
AUC	—
ACC	$m e t r i c s A C C = r i g h t N$
RMSE	$m e t r i c s R M S E = 1 n ∑ i = 1 n y i - h i 2$
$R 2$	$m e t r i c s R 2 = 1 - ∑ i = 1 n (y i - h i) 2 ∑ i = 1 n (y i - h -) 2$
MAE	$m e t r i c s M A E = 1 n ∑ i = 1 n \| y i - h i \|$
LL	$m e t r i c s L L = ∑ i = 1 n [y i l g h i + (1 - y i) l g (1 - h i)]$

表5 常用的评估指标

Table 5 Commonly used evaluation indicators

Specific metric	Formula mode
AUC	—
ACC	$m e t r i c s A C C = r i g h t N$
RMSE	$m e t r i c s R M S E = 1 n ∑ i = 1 n y i - h i 2$
$R 2$	$m e t r i c s R 2 = 1 - ∑ i = 1 n (y i - h i) 2 ∑ i = 1 n (y i - h -) 2$
MAE	$m e t r i c s M A E = 1 n ∑ i = 1 n \| y i - h i \|$
LL	$m e t r i c s L L = ∑ i = 1 n [y i l g h i + (1 - y i) l g (1 - h i)]$

表6 模型比较

Table 6 Model comparison

模型大类	提出时间	原理	优势	局限性	适用场景
BKT	1994	HMM	模型简单，具有可靠的教学可解释性	依赖教育专家标注矩阵以及简化的假设	适用于根据先验知识状态自动给每个学生推荐题目的场景，需要先得到先验分布
FAM	2006	Logistic模型	模型简单，增加练习-KC的Q矩阵，具有可靠的教学可解释性	依赖教育专家标注矩阵，需要手工输入特征	适用于从历史数据中学习一般参数对学生建模进而预测作答表现的场景，需要教育专家标注的Q矩阵
DKT	2015	RNN/LSTM	性能较优，自动输入特征学习，无需专家对KC进行显示编码	模型复杂，训练规模较大，不具备教学可解释性	适用于不需要解释学生知识状态、只需给出学生学习结果情况的场景，如智能组卷场景
DKVMN	2017	MANN	网络相对简单，提高了模型的记忆能力	参数较多，训练规模大	适用于学生日常练习记录交互日志，在练习-KC单一映射的场景下快速建立学生知识状态的掌握情况
GKT	2019	GNN	建模底层KC之间的关系图，具有一定的可解释性	实际教学中KC划分粒度不一致直接影响学生知识状态的评估性能	适用于练习-KC之间存在多重复杂关系的场景，对学生知识状态掌握情况的细节要求较高，具备一定的可解释性

表7 模型性能对比概览

Table 7 Overview of model performance %

方法	ASSIST2009	ASSIST2012	ASSIST2015	ASSIST2017	KDD Cup 2010	Statics2011	Synthetic-5	slepemapy.cz	EdNet	Junyi
BKT	67.00	—	—	—	—	—	—	—	—	—
BKT+	—	—	—	—	—	—	80.00	—	—	—
PFA	70.00	—	—	—	—	—	—	—	—	—
IRT	73.00	73.17	—	—	—	68.00	—	—	—	—
KTM	81.86	—	—	—	—	—	—	—	—	—
RKTM	76.50	76.90	72.62	—	—	83.39	81.86	—	—	—
DKT	86.00	—	72.52	—	—	80.20	75.00	—	—	—
DKT+	82.27	—	73.71	73.43	—	83.49	82.64	—	—	—
DKT+HFE	74.70	—	—	—	—	—	—	—	—	73.30
DKT-DSC	91.00	87.00	87.00	—	81.00	—	—	—	—	—
PDKT-C	78.00	—	—	—	—	—	—	—	—	—
DHKT	78.66	77.47	—	—	—	83.33	—	—	—	—
DKT+FB	—	73.09	—	—	—	—	—	80.46	—	—
DKT LSTM	73.68	—	—	—	—	68.15	—	—	—	—
DynEmb	73.90	73.60	—	—	86.80	—	—	—	—	—
LANA	—	—	—	—	—	—	—	—	80.59	—
DKVMN	81.57	—	72.68	—	—	82.84	82.73	—	—	—
Deep-IRT	81.65	—	72.88	—	—	83.09	82.98	—	—	—
LPKT	82.35	—	73.83	—	—	—	—	—	—	—
DKVMN-LA	91.90	—	—	—	—	—	—	—	—	—
CKT	82.54	—	72.91	—	—	82.41	82.45	—	—	—
KQN	82.32	—	73.40	—	—	83.20	82.81	—	—	—
HMN	82.73	—	73.01	73.10	—	83.51	—	—	—	—
GKT	72.30	—	—	—	76.90	—	—	—	—	—
GIKT	78.96	77.54	—	—	—	—	—	—	75.23	—
JKT	79.80	—	76.50	74.50	83.40	85.60	85.90	—	—	—
DGMN	86.10	—	—	—	—	86.40	—	—	—	—
SAKT	84.80	—	85.40	73.40	—	85.30	83.20	—	—	—
SAINT	—	—	—	—	—	—	—	—	78.11	—
AKT	83.46	—	78.28	77.02	—	82.68	—	—	—	—
RKT	—	79.30	—	—	—	—	—	—	—	86.00
MF-DAKT	85.10	—	—	—	—	—	—	—	77.60	—
ATKT	82.44	—	80.45	72.97	—	83.25	—	—	—	—

表7 模型性能对比概览

Table 7 Overview of model performance %

方法	ASSIST2009	ASSIST2012	ASSIST2015	ASSIST2017	KDD Cup 2010	Statics2011	Synthetic-5	slepemapy.cz	EdNet	Junyi
BKT	67.00	—	—	—	—	—	—	—	—	—
BKT+	—	—	—	—	—	—	80.00	—	—	—
PFA	70.00	—	—	—	—	—	—	—	—	—
IRT	73.00	73.17	—	—	—	68.00	—	—	—	—
KTM	81.86	—	—	—	—	—	—	—	—	—
RKTM	76.50	76.90	72.62	—	—	83.39	81.86	—	—	—
DKT	86.00	—	72.52	—	—	80.20	75.00	—	—	—
DKT+	82.27	—	73.71	73.43	—	83.49	82.64	—	—	—
DKT+HFE	74.70	—	—	—	—	—	—	—	—	73.30
DKT-DSC	91.00	87.00	87.00	—	81.00	—	—	—	—	—
PDKT-C	78.00	—	—	—	—	—	—	—	—	—
DHKT	78.66	77.47	—	—	—	83.33	—	—	—	—
DKT+FB	—	73.09	—	—	—	—	—	80.46	—	—
DKT LSTM	73.68	—	—	—	—	68.15	—	—	—	—
DynEmb	73.90	73.60	—	—	86.80	—	—	—	—	—
LANA	—	—	—	—	—	—	—	—	80.59	—
DKVMN	81.57	—	72.68	—	—	82.84	82.73	—	—	—
Deep-IRT	81.65	—	72.88	—	—	83.09	82.98	—	—	—
LPKT	82.35	—	73.83	—	—	—	—	—	—	—
DKVMN-LA	91.90	—	—	—	—	—	—	—	—	—
CKT	82.54	—	72.91	—	—	82.41	82.45	—	—	—
KQN	82.32	—	73.40	—	—	83.20	82.81	—	—	—
HMN	82.73	—	73.01	73.10	—	83.51	—	—	—	—
GKT	72.30	—	—	—	76.90	—	—	—	—	—
GIKT	78.96	77.54	—	—	—	—	—	—	75.23	—
JKT	79.80	—	76.50	74.50	83.40	85.60	85.90	—	—	—
DGMN	86.10	—	—	—	—	86.40	—	—	—	—
SAKT	84.80	—	85.40	73.40	—	85.30	83.20	—	—	—
SAINT	—	—	—	—	—	—	—	—	78.11	—
AKT	83.46	—	78.28	77.02	—	82.68	—	—	—	—
RKT	—	79.30	—	—	—	—	—	—	—	86.00
MF-DAKT	85.10	—	—	—	—	—	—	—	77.60	—
ATKT	82.44	—	80.45	72.97	—	83.25	—	—	—	—

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面向智慧教育的知识追踪模型研究综述

Review of Knowledge Tracing Model for Intelligent Education

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