论文标题
学习大型$ Q $ -Matrix由受限的玻尔兹曼机器
Learning Large $Q$-matrix by Restricted Boltzmann Machines
论文作者
论文摘要
在认知诊断模型（CDM）中估计具有许多项目和来自观察数据的潜在属性的大$ Q $ -Matrix，由于其高计算成本，这是一个巨大的挑战。从深度学习文献中借用想法，我们建议通过受限的玻尔兹曼机器（RBMS）学习大型$ Q $ -Matrix，以克服计算困难。在本文中，确定了RBM和CDM之间的关键关系。在某些条件下，对各种CDM中的$ Q $ -Matrix进行一致且强大的学习被证明是有效的。我们在不同CDM设置下的模拟研究表明，RBM不仅在学习速度方面优于现有方法，而且还保持$ Q $ -MATRIX的良好恢复精度。最后，我们通过对Cattell的16个人格测试数据集的真实数据分析来说明我们方法的适用性和有效性。
Estimation of the large $Q$-matrix in Cognitive Diagnosis Models (CDMs) with many items and latent attributes from observational data has been a huge challenge due to its high computational cost. Borrowing ideas from deep learning literature, we propose to learn the large $Q$-matrix by Restricted Boltzmann Machines (RBMs) to overcome the computational difficulties. In this paper, key relationships between RBMs and CDMs are identified. Consistent and robust learning of the $Q$-matrix in various CDMs is shown to be valid under certain conditions. Our simulation studies under different CDM settings show that RBMs not only outperform the existing methods in terms of learning speed, but also maintain good recovery accuracy of the $Q$-matrix. In the end, we illustrate the applicability and effectiveness of our method through a real data analysis on the Cattell's 16 personality test data set.
