用连续变量贝叶斯网络实时追踪学生技能掌握度并给出可信度
Tracking student skills real-time through a continuous-variable dynamic Bayesian network
- 基于连续变量的动态贝叶斯网络，实时更新技能掌握分布
- 引入贝塔分布共轭先验，实现解析式在线更新，计算高效
- 不仅能预测答题正确率，还提供估计置信度，适合教育系统部署
知识追踪旨在预测学生在特定技能上的表现成功率。现代方法如深度知识追踪虽精度高，但依赖神经网络难以解释；传统动态贝叶斯网络可解释性强，却因计算量大难以实时更新，且无法提供估计准确性数据。本文提出性能分布追踪（PDT）方法，采用以连续随机变量为节点的动态贝叶斯网络，实时追踪成功率的分布。通过跟踪分布，始终可获取估计的置信度信息，并能融合相关技能数据生成更精准的预测。该方法支持组合技能题目预测，在使用贝塔分布作为共轭先验的情况下，所有分布均可解析表达，实现高效在线更新。实验表明，用户普遍认为其预测结果足够可信，愿意采纳基于此的推荐。
原文摘要 · Abstract (English)
The field of Knowledge Tracing is focused on predicting the success rate of a student for a given skill. Modern methods like Deep Knowledge Tracing provide accurate estimates given enough data, but being based on neural networks they struggle to explain how these estimates are formed. More classical methods like Dynamic Bayesian Networks can do this, but they cannot give data on the accuracy of their estimates and often struggle to incorporate new observations in real-time due to their high computational load. This paper presents a novel method, Performance Distribution Tracing (PDT), in which the distribution of the success rate is traced live. It uses a Dynamic Bayesian Network with continuous random variables as nodes. By tracing the success rate distribution, there is always data available on the accuracy of any success rate estimation. In addition, it makes it possible to combine data from similar/related skills to come up with a more informed estimate of success rates. This makes it possible to predict exercise success rates, providing both explainability and an accuracy indication, even when an exercise requires a combination of different skills to solve. And through the use of the beta distribution functions as conjugate priors, all distributions are available in analytical form, allowing efficient online updates upon new observations. Experiments have shown that the resulting estimates generally feel sufficiently accurate to end-users such that they accept recommendations based on them.
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