Saturated diagnostic classification models (DCM) can flexibly accommodate various relationships among attributes to diagnose individual attribute mastery, and include various important DCMs as sub-models. However, the existing formulations of the saturated DCM are not better suited for deriving conditionally conjugate priors of model parameters. Because their derivation is the key in developing a variational Bayes (VB) inference algorithm, in the present study, we proposed a novel mixture formulation of saturated DCM. Based on it, we developed a VB inference algorithm of the saturated DCM that enables us to perform scalable and computationally efficient Bayesian estimation. The simulation study indicated that the proposed algorithm could recover the parameters in various conditions. It has also been demonstrated that the proposed approach is particularly suited to the case when new data become sequentially available over time, such as in computerized diagnostic testing. In addition, a real educational dataset was comparatively analyzed with the proposed VB and Markov chain Monte Carlo (MCMC) algorithms. The result demonstrated that very similar estimates were obtained between the two methods and that the proposed VB inference was much faster than MCMC. The proposed method can be a practical solution to the problem of computational load.

中文翻译：

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饱和诊断分类模型的变分贝叶斯推理算法

饱和诊断分类模型（DCM）可以灵活地容纳属性之间的各种关系来诊断单个属性的掌握情况，并包括各种重要的DCM作为子模型。然而，饱和 DCM 的现有公式并不更适合推导模型参数的条件共轭先验。由于它们的推导是开发变分贝叶斯 (VB) 推理算法的关键，因此在本研究中，我们提出了一种新的饱和 DCM 混合公式。在此基础上，我们开发了饱和 DCM 的 VB 推理算法，使我们能够执行可扩展且计算效率高的贝叶斯估计。仿真研究表明，该算法可以在各种条件下恢复参数。还表明，所提出的方法特别适用于新数据随着时间的推移依次可用的情况，例如在计算机化诊断测试中。此外，还使用所提出的 VB 和马尔可夫链蒙特卡罗 (MCMC) 算法对真实的教育数据集进行了比较分析。结果表明，两种方法获得了非常相似的估计，并且所提出的 VB 推理比 MCMC 快得多。所提出的方法可以成为解决计算负载问题的实用解决方案。结果表明，两种方法获得了非常相似的估计，并且所提出的 VB 推理比 MCMC 快得多。所提出的方法可以成为解决计算负载问题的实用解决方案。结果表明，两种方法获得了非常相似的估计，并且所提出的 VB 推理比 MCMC 快得多。所提出的方法可以成为解决计算负载问题的实用解决方案。