面向大规模认知诊断的DINA模型快速计算方法研究

在教育教学的过程中，如何诊断学生的知识水平是一个重要的问题.传统方法大多由教师根据学生的表现和成绩进行人工判断，存在效率低、主观性强的问题，且难以做到针对大量学生的个性化诊断.近年来，认知诊断模型中的DINA模型被广泛应用于诊断学生个性化知识掌握程度.然而传统DINA模型大多基于小样本数据，当面对在线教育带来的大规模数据处理需求时，存在收敛速度慢的问题，难以实际应用.针对DINA模型计算时间过长的问题，本文首先给出了DINA模型的收敛性证明，并提出了三种能够加速DINA求解的算法：（1）增量算法，它将学生数据划分为多个学生块，每次迭代只访问其中一个学生块；（2）最大熵方法，它只访问在极大化模型熵的过程中影响较大的学生数据；（3）基于前两者的混合方法.最后，本文通过真实数据和模拟数据上的实验，分析证明了三种方法均能在保证DINA模型有效性的情况下，达到几倍至几十倍的加速效果，有效地改善了DINA模型的计算效率.

The Rapid Calculation Method of DINA Model for Large Scale Cognitive Diagnosis

How to assess students' cognitive structure is an important problem in the process of education and teaching.Traditionally,teachers evaluate a student based on their classroom performance and scores,which is lack of efficiency,objectivity,and it is hard to treat anyone equally.To solve this problem,DINA model,which is able to evaluate knowledge proficiency of students,has become a popular Cognitive Diagnosis model with a good interpretation.However,traditional DINA models are all based on small samples.When it comes to large-scale online learning scenario,the calculation will be significantly time-consuming.To address these issues,we first give proof of the convergence of DINA model,and then propose three acceleration methods.To be specific,the first one,called Incremental DINA(I-DINA),can partition the student data into blocks and iterate through the blocks.Then the second one,Maximum-Entropy DINA(ME-DINA),can choose and only access the most powerful students.At last,we combine the advantages of these two methods and propose the last model called Incremental Maximum Entropy DINA(IME-DINA).Extensive experiments on both a real-world dataset and simulation data demonstrate that our models can achieve dozens of acceleration without reducing the effectiveness of DINA Model.