用新推断方法提升薄弱数据下数学考试预测准确率
Accurate Predictions in Education with Discrete Variational Inference
- 基于项目反应理论构建概率模型，结合离散变分推断
- 在低数据场景下达80%以上准确率，超越传统方法
- 发现单一能力参数即可实现最优预测，适合教育AI研发
社会不平等的重要根源之一是个性化辅导资源获取不均，富裕群体可负担辅导，多数人则不能。低成本高效的AI导师系统可提供规模化解决方案。本文聚焦自适应学习中的关键问题：预测学生是否能正确回答题目，这是有效辅导系统的核心。然而，许多平台在数据稀疏场景下难以实现高精度预测。为此，我们发布了迄今最大的公开专业标记的正式数学考试答题数据集。提出一种基于项目反应理论（IRT）的概率建模框架，在正式考试答题预测上达到超过80%的准确率，创下新基准。进一步扩展的协同过滤模型引入主题级技能画像，却揭示了一个出人意料且具有教育意义的发现：仅需一个潜在能力参数即可实现最高预测精度。本文主要贡献在于推导并实现了新颖的离散变分推断框架，在低数据条件下取得最高预测准确率，显著优于所有经典IRT与矩阵分解基线方法。
原文摘要 · Abstract (English)
One of the largest drivers of social inequality is unequal access to personal tutoring, with wealthier individuals able to afford it, while the majority cannot. Affordable, effective AI tutors offer a scalable solution. We focus on adaptive learning, predicting whether a student will answer a question correctly, a key component of any effective tutoring system. Yet many platforms struggle to achieve high prediction accuracy, especially in data-sparse settings. To address this, we release the largest open dataset of professionally marked formal mathematics exam responses to date. We introduce a probabilistic modelling framework rooted in Item Response Theory (IRT) that achieves over 80 percent accuracy, setting a new benchmark for mathematics prediction accuracy of formal exam papers. Extending this, our collaborative filtering models incorporate topic-level skill profiles, but reveal a surprising and educationally significant finding, a single latent ability parameter alone is needed to achieve the maximum predictive accuracy. Our main contribution though is deriving and implementing a novel discrete variational inference framework, achieving our highest prediction accuracy in low-data settings and outperforming all classical IRT and matrix factorisation baselines.
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