发表机构
School of Computer and Cyber Sciences, Augusta University; School of Computing, University of Georgia; Department of Graduate Psychology, James Madison University; Department of Computer Science and Engineering, University of Tennessee at Chattanooga; Department of Radiology, Massachusetts General Hospital, Harvard Medical School（奥古斯塔大学计算机与网络科学学院; 佐治亚大学计算学院; 詹姆斯麦迪逊大学研究生心理学系; 田纳西大学查塔努加分校计算机科学与工程系; 哈佛医学院麻省总医院放射科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究首次将量子机器学习应用于认知诊断的Q矩阵估计，提出量子稀疏自编码器，经60个模拟及9个真实测评数据集测试，其相比经典自编码器更稳定、在多数真实数据集上表现更优。
AI 中文摘要
Q矩阵在教育数据挖掘（EDM）的认知诊断中处于核心地位，用于指定每个测评项目所需的潜在技能。当测评涉及大量相关技能，且实际作答模式偏离理想化生成假设时，数据驱动的Q矩阵估计仍具挑战性。我们提出一种新型量子稀疏自编码器（QSAE）用于Q矩阵估计，据我们所知，这是量子机器学习（QML）在认知诊断中的首次应用。总体而言，QSAE通过编码器将每个学生的二元作答向量嵌入量子电路，压缩为稀疏潜在表示，再将该表示映射到Q矩阵。我们在60个模拟数据集和9个真实测评数据集上将QSAE与经典自编码器（CAE）进行基准测试。结果显示二者各有优势：尽管CAE在若干模拟条件下部分达到更高平均准确率，但QSAE在重复实验中显著更稳定，在60个条件中的49个条件下表现出更低方差；此外，在真实测评数据上，QSAE在9个数据集中的6个上优于CAE。这些发现表明，QML在此场景下的主要进展并非通用准确率提升，而是增强了鲁棒性，以及探索真实数据集潜在结构复杂性的能力。
英文摘要
Q-matrices play a central role in cognitive diagnosis within educational data mining (EDM), specifying which latent skills each assessment item requires. Data-driven Q-matrix estimation remains challenging when assessments involve many correlated skills and when real response patterns depart from idealized generative assumptions. We introduce a novel quantum sparse autoencoder (QSAE) for Q-matrix estimation, which, to the best of our knowledge, is the first application of quantum machine learning (QML) to cognitive diagnosis. Overall, the QSAE embeds each student's binary response vector into a quantum circuit using an encoder, compresses it into a sparse latent representation, and maps that representation to the Q-matrix. We benchmark the QSAE against a classical autoencoder (CAE) across 60 simulated datasets and 9 real-world assessment datasets. The results reveal complementary strengths. Although the CAE partially achieves higher average accuracy under several simulation conditions, the QSAE is substantially more stable across replications, exhibiting lower variance in 49 of the 60 conditions. Moreover, on real assessment data, the QSAE outperforms the CAE on 6 of the 9 datasets. These findings suggest that the principal advancement of QML in this setting is not universal accuracy improvement, but enhanced robustness and capability to explore latent-structure complexity in real datasets.
