Personalized Learning Path Recommendation via Causality-inspired Debiasing and Hyperbolic Representation
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摘要: 教育推荐系统在实际应用中主要面临三类挑战: 一是学生学习行为中普遍存在刷题效应和随机猜测等混淆因素, 易导致模型学习到虚假相关性而偏离隐含的因果机制; 二是知识点之间具有显著的层级依赖与先后结构, 传统欧氏表示难以有效刻画其内在层次关系; 三是现有方法在路径生成过程中忽略学习决策对学生知识状态的影响, 导致推荐路径连贯性不足. 为解决上述问题, 提出一种融合因果启发式去偏与双曲表示的个性化学习路径推荐框架(CHPLR), 通过两阶段建模实现因果去偏、层次建模与路径优化的协同优化. 在第一阶段, 构建学生—练习题—知识点异构图, 利用因果推断削弱刷题频率和随机猜测等混淆因素的干扰, 从而学习更加因果纯净的学生与知识表示; 在此基础上, 第二阶段将去偏后的图结构映射至双曲空间, 借助其天然的层次特性刻画知识点间的递进与依赖关系, 并结合反事实评估设计因果感知的路径规划策略, 在保证知识结构合理性的同时, 优先选择具有更高因果增益的学习序列, 从而提升整体学习效率. 在Junyi、ASSISTments与Math三个真实教育数据集上的实验结果表明,CHPLR在推荐准确率、路径质量及因果一致性等指标上均优于现有基准模型, 且消融实验与鲁棒性分析进一步验证了各模块的有效性与框架整体设计的合理性.Abstract: Educational recommender systems face three major challenges in practical applications. First, student learning behaviors are affected by confounding factors such as the practice effect and random guessing, which may lead models to learn spurious correlations rather than the underlying causal mechanisms. Second, knowledge concepts exhibit significant hierarchical dependencies and prerequisite relationships that are difficult to capture with conventional Euclidean representations. Third, existing methods overlook the impact of learning decisions on students’ knowledge states during path generation, resulting in insufficient coherence of recommended learning paths. To address these challenges, we propose a framework that integrates causality-inspired debiasing and hyperbolic representations(CHPLR). Through two-stage modeling, the framework jointly achieves causal debiasing, hierarchical modeling, and learning path optimization. In the first stage, we construct a student–question–knowledge heterogeneous graph and employ causal inference to mitigate the interference of confounding factors, such as the practice effect and random guessing, thereby learning causally purified representations of students and knowledge concepts. In the second stage, the debiased graph structure is mapped into hyperbolic space to capture the hierarchical dependencies and prerequisite relationships among knowledge concepts, while a causality-aware path planning strategy based on counterfactual evaluation prioritizes learning sequences with higher causal gains while maintaining the rationality of the knowledge structure, thereby improving learning efficiency. Experiments on three real-world educational datasets(Junyi, ASSISTments, and Math) show that CHPLR outperforms existing baseline models in recommendation accuracy, learning path quality, and causal consistency. Ablation experiments and robustness analyses further validate the effectiveness of each module and the rationality of the overall framework.1)
1 https://sites.google.com/site/ASSISTmentsdata/home/2009-2010-assistment-data2)2 https://www.zhixue.com3)3 https://pslcdatashop.web.cmu.edu/DatasetInfo?datasetId=1198 -
图 3 因果启发式去偏与双曲表示的个性化学习路径推荐框架
Fig. 3 Personalized learning path recommendation framework that integrates causality-inspired debiasing with hyperbolic representation
图 5 去噪前后的因果关系热力图和t-SNE分布
Fig. 5 Causal relationship heatmaps and t-SNE distributions before and after denoising
图 6 不同扰动强度$ \sigma$下各模块的误差传播情况
Fig. 6 Error propagation of each module under different perturbation intensities $ \sigma$
图 8 不同学习阶段学生群体上的性能变化情况
Fig. 8 Performance variation of student groups across different learning stages
图 9 欧氏空间与双曲空间中的推荐学习路径示例
Fig. 9 Examples of recommended learning paths in Euclidean and hyperbolic spaces
表 1 数据集的基本统计信息
Table 1 Basic statistical information of the datasets
数据集 ASSISTments Math Junyi #学生 4163 10268 10,000 #练习练习题 17746 917495 835 #知识点 123 1488 835 #回答日志 324572 864722 353835 
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表 2 模型在Junyi数据集上的性能对比
Table 2 Performance comparison of models on Junyi dataset
模型 AUC ACC F1 LightGCN 0.8431 ±0.0053 0.7819 ±0.0049 0.7428 ±0.0056 EHGCN 0.8342 ±0.0057 0.7625 ±0.0051 0.7509 ±0.0048 KFGAN 0.8701 ±0.0042 0.8098 ±0.0039 0.7879 ±0.0045 DEKGCI 0.8794 ±0.0039 0.7987 ±0.0041 0.8251 ±0.0037 IDRMI 0.9008 ±0.0035 0.8519 ±0.0033 0.8129 ±0.0038 DHCF 0.8172 ±0.0064 0.7588 ±0.0059 0.7205 ±0.0067 HCCF 0.8549 ±0.0048 0.7926 ±0.0045 0.7604 ±0.0050 CHPLR 0.9099 ±0.0026 0.8681 ±0.0028 0.8523 ±0.0030
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表 3 模型在ASSISTments数据集上的性能对比
Table 3 Performance comparison of models on ASSISTments dataset
模型 AUC ACC F1 LightGCN 0.7896 ±0.0062 0.7221 ±0.0058 0.6819 ±0.0065 EHGCN 0.7768 ±0.0068 0.7101 ±0.0061 0.6712 ±0.0070 KFGAN 0.8241 ±0.0051 0.7372 ±0.0054 0.7021 ±0.0058 DEKGCI 0.8052 ±0.0055 0.7238 ±0.0052 0.6831 ±0.0059 IDRMI 0.8491 ±0.0044 0.7728 ±0.0046 0.7398 ±0.0048 DHCF 0.7759 ±0.0075 0.7087 ±0.0069 0.6676 ±0.0077 HCCF 0.8131 ±0.0053 0.7252 ±0.0056 0.6923 ±0.0061 CHPLR 0.8407 ±0.0038 0.7979 ±0.0035 0.7691 ±0.0039
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表 4 模型在Math数据集上的性能对比
Table 4 Performance comparison of models on Math dataset
模型 AUC ACC F1 LightGCN 0.7331 ±0.0081 0.6654 ±0.0075 0.6264 ±0.0084 EHGCN 0.7175 ±0.0090 0.6418 ±0.0082 0.6098 ±0.0093 KFGAN 0.7635 ±0.0068 0.6721 ±0.0072 0.6636 ±0.0069 DEKGCI 0.7438 ±0.0075 0.6632 ±0.0078 0.6493 ±0.0076 IDRMI 0.7989 ±0.0057 0.7078 ±0.0062 0.6551 ±0.0064 DHCF 0.7136 ±0.0096 0.6279 ±0.0089 0.6032 ±0.0098 HCCF 0.7389 ±0.0071 0.6648 ±0.0075 0.6271 ±0.0080 CHPLR 0.8011 ±0.0049 0.7172 ±0.0052 0.6988 ±0.0055
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表 5 消融实验结果
Table 5 The results of ablation experiment
模型消融版本 AUC ACC F1 w/o CD&HR 0.7023 0.6892 0.6502 w/o CD 0.7432 0.7268 0.7116 w/o HR 0.7736 0.7418 0.7257 w/o OR 0.8079 0.7631 0.7214 CHPLR 0.8407 0.7979 0.7691
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表 6 未观测混杂敏感性分析——潜在表示扰动
Table 6 Sensitivity analysis for unobserved confounders: Latent representation perturbation
混杂强度$\gamma$ $\Delta_{\text{ATE}}^{\text{conf}}$ $\Delta_{\text{CDN}}^{\text{conf}}$ FlipRate(%) $\Delta_{\text{Rec}}^{\text{conf}}$ 0(基准) 0 0 0 0 0.02 0.0031 0.0028 0.41 0.0008 0.05 0.0074 0.0065 0.97 0.0019 0.10 0.0163 0.0141 2.13 0.0047 0.15 0.0289 0.0247 3.86 0.0091
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表 7 未观测混杂敏感性分析——边权扰动
Table 7 Sensitivity analysis for unobserved confounders: Edge weight perturbation
扰动范围$\rho$ $\Delta_{\text{ATE}}^{\text{conf}}$ $\Delta_{\text{CDN}}^{\text{conf}}$ FlipRate(%) $\Delta_{\text{Rec}}^{\text{conf}}$ 0(基准) 0 0 0 0 0.05 0.0024 0.0021 0.33 0.0006 0.10 0.0058 0.0051 0.79 0.0015 0.20 0.0134 0.0118 1.84 0.0038 0.30 0.0241 0.0213 3.27 0.0074
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表 8 Bootstrap参数稳定性分析
Table 8 Bootstrap-based parameter stability analysis
数据集 $\overline{W}_{\theta}$ $\overline{W}_{{\cal{D}}}$ 相对宽度(%) Junyi 0.0331 0.0294 3.31 ASSISTments 0.0468 0.0387 4.68 Math 0.0517 0.0435 5.17
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表 9 $ K$和$ \epsilon$的敏感性实验
Table 9 Sensitivity experiments on $ K$ and $ \epsilon$
实验组 $K$ $\epsilon$ AUC ACC ATE 变$K$-1 1 0.10 0.8868 0.8542 0.0305 变$K$-2 5 0.10 0.8996 0.8614 0.0312 变$K$-3 7 0.10 0.8891 0.8569 0.0317 变$\epsilon$-1 3 0.05 0.8975 0.8553 0.0308 变$\epsilon$-2 3 0.15 0.8958 0.8619 0.0313 变$\epsilon$-3 3 0.20 0.8927 0.8635 0.0321 基准 3 0.10 0.9099 0.8681 0.0332
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表 10 m和$ \tau$的敏感性实验
Table 10 Sensitivity experiments on m and $ \tau$
实验组 $m$ $\tau$ 保留边比例 AUC ATE 变$m$-1 1 0.10 0.52 0.8631 0.0298 变$m$-2 2 0.10 0.68 0.8887 0.0315 变$m$-3 4 0.10 0.81 0.8692 0.0323 变$\tau$-1 3 0.05 0.82 0.8719 0.0311 变$\tau$-2 3 0.15 0.69 0.8896 0.0318 变$\tau$-3 3 0.20 0.63 0.8931 0.0306 基准 3 0.10 0.74 0.9099 0.0332
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表 11 复杂度分析符号定义
Table 11 Symbol definitions for complexity analysis
符号 含义 $|{\cal{D}}|$ 答题记录总数 $|{S}|$, $|{Q}|$, $|{K}|$ 学生、练习题、知识点数量 $|{E}_{SQ}|$, $|{E}_{QK}|$, $|{E}_{KK}|$ 三类边数量 $|{E}|$ 总边数, $|{E}_{SQ}|+|{E}_{QK}|+|{E}_{KK}|$ $|{E}_{\text{pure}}|$ 因果净化后边数, $|{\cal{E}}_{\text{pure}}| \leq |{E}|$ $d_{\text{cog}}$ 认知诊断维度 $d$ 双曲嵌入维度 $d_h$ CDN与NCDM隐层维度 $L_{mlp}$ NCDM中MLP层数 $L$ 双曲图卷积层数 $K$ PSM近邻数($K=3$) $B$ 后门调整分层数($B=5$) $|{\cal{F}}_i|$ 学生$s_i$的学习前沿大小 $L_{\text{path}}$ 推荐路径长度 $|{\cal{N}}(s_i)|$ 学生$s_i$的邻居练习题数
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表 12 各模块计算复杂度汇总
Table 12 Summary of computational complexity for each module
模块 时间复杂度 主要瓶颈 NCDM $\mathrm{O}(|{\cal{D}}| L_{mlp} d_h^2)$ 数据规模 PSM(优化) $\mathrm{O}(|{E}_{SQ}| \log|{S}| + |{E}_{QK}|)$ 边规模 后门调整+反事实 $\mathrm{O}(|{E}_{SQ}| d_{\text{cog}} + |{S}|)$ 边规模 CDN $\mathrm{O}(|{E}| d_h^2)$ 边规模 噪声边剔除 $\mathrm{O}(|{E}|)$ 边规模 双曲图卷积 $\mathrm{O}(L(|{E}_{\text{pure}}| d + |{V}| d^2))$ 图规模、维度 路径搜索(A*) $\mathrm{O}(|{\cal{F}}_i| L_{\text{path}} \log|{\cal{F}}_i|)$ 前沿大小 CATE验证 $\mathrm{O}(L_{\text{path}} |S_j| d_{\text{cog}})$ 路径长度 在线更新 $\mathrm{O}(|{\cal{N}}(s_i)| d + d_h^2)$ 邻居数 训练阶段总计 $\mathrm{O} \left(|{\cal{D}}| L_{mlp} d_h^2 + |{E}_{SQ}| \log|{S}| + |{E}| d_h^2 + L |{E}_{\text{pure}}| d + L |{V}| d^2\right)$ 推理阶段总计 $\mathrm{O} \left(|{K}| d + |{\cal{F}}_i| L_{\text{path}} \log|{\cal{F}}_i|\right)$ 在线更新总计 $\mathrm{O} \left(|{\cal{N}}(s_i)| d + d_h^2\right)$, 与全局图规模无关
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