Heterogeneous Graph Neural Networks for Concept Prerequisite Relation Learning in Educational Data (2021)

Abstract: Prerequisite relations among concepts are crucial for educational applications, such as curriculum planning and intelligent tutoring. In this paper, we propose a novel concept prerequisite relation learning approach, named CPRL, which combines both concept representation learned from a heterogeneous graph and concept pairwise features. Furthermore, we extend CPRL under weakly supervised settings to make our method more practical, including learning prerequisite relations from learning object dependencies and generating training data with data programming. Our experiments on four datasets show that the proposed approach achieves the state-of-the-art results comparing with existing methods.

## introduction with the increasing availability of learning resources and the requirement of self-regulated learning, there is a rising need to organize knowledge in a reasonable order. concept prerequisite relations are essentially considered as the dependency among concepts, and they are crucial for people to learn, organize, apply and generate knowledge @xcite . for example, if someone wants to learn the knowledge about conditional random fields, the knowledge about hidden markov model should be learned first. consequently, the concept hidden markov model is a prerequisite concept of the concept conditional random fields. nowadays, prerequisite relations among concepts have played a crucial role in educational applications, such as curriculum planning @xcite and intelligent tutoring @xcite . recently, several attempts have been made to extract prerequisite relations among concepts from textbooks @xcite , moocs (massive open online courses) @xcite , courses @xcite @xcite @xcite and scientific papers @xcite . they either proposed a local statistical information, such as reference distance @xcite and cross-entropy @xcite to measure the prerequisite relations between concepts, or proposed handcrafted features to learn a prerequisite relation classifier @xcite . @xcite proposed cpr-recover to recover concept prerequisite relations from course dependencies. more recently, @xcite applied variational graph autoencoders to learn concept prerequisite relations from courses. while @xcite developed a supervised learning approach called prereq. however, there are still several challenges to learn the prerequisite relations among concepts. firstly, there are multiple and complex relations among concepts and learning resources, but they were not fully utilized before. secondly, labeling training data is enormously expensive and time consuming, especially when domain expertise is required for concept prerequisite relation judgement. in order to address these challenges, we propose a novel concept prerequisite relation learning approach, named cprl, which firstly learns concept representation via a relational graph convolutional network (r-gcn) @xcite on a heterogeneous graph, and predicts the concept prerequisite relations with a siamese network. then, it is optimized with the learning object dependencies and handcrafted features. moreover, we extend cprl under the weaklysupervised settings to make our approach more practical, including learning prerequisite relation from learning object dependencies and generating training data with data programming paradigm. our contributions can be summarized as follows: ## problem formulation the educational data can be a textbook or a course, which can be modeled as a sequential learning objects (denoted as lo for short), such as book chapters, mooc videos and lectures. there are concepts in an educational data, and we would like to extract the prerequisite relation among these concepts, as shown in figure 1 . …… lectures graph minimal spanning tree kruskal's algorithm figure 1: an example of prerequisite relation learning for concepts in educational data. for convenience, we will use the following notations: therefore, the problem could be formally defined as: given an educational data d and its corresponding concepts c, the goal is to learn a function f θ : c × @xmath0, 1}, which can predict whether c i is a prerequisite concept of c j by mapping the concept pair c i , c j to a binary class. ## the cprl framework the overview of our proposed cprl is shown in figure 2 . we firstly build a heterogeneous conceptlearning object graph from the educational data, and then use a relational graph convolutional network (r-gcn) @xcite to represent the concepts and learning objects. then, pairwise features for concepts are extracted according to their textual and structural information. finally, all features are combined to learn the concept prerequisite relations. it should be noted that the dependencies among learning objects can be viewed as a signal of weak supervision, which are also used to train the model. ## the cprl with weak supervision in practice, it is expensive to collect massive handlabeled data for model training. one intuitive way to alleviate the labeling cost is that we can train the model in one domain (e.g. calculus), and then use it to predict the concept prerequisite relations in other domains (e.g. data structure and physics). however, the idea fails and we will explain it in our experiments. therefore, we extend our model under the weak supervision settings in two ways. we call the first way as learning prerequisite relations from lo dependencies. since concepts and los are embedded into the same space through r-gcn in the heterogeneous graph, our model can implicitly infer the prerequisite relationships between concepts by explicitly learning the dependencies between los. this procedure is called cprl lo . another way is use the data programming (ratner et al., 2016) paradigm to create probabilistic training data. data programming expresses weak supervision strategies or domain heuristics as labeling functions (lfs), and then estimates the label accuracies by fitting a generative model. the process is shown as figure 4 . ## conclusion in this paper, we propose a novel concept prerequisite relation learning approach, named cprl, which combines both concept representation learned from a heterogeneous graph and concept pairwise features. furthermore, we extend cprl under weakly supervised settings to make our method more practical. the experiments on four datasets show that our method achieves stateof-the-art performance. in addition, we also prove the effectiveness of our weakly supervised prerequisite relation learning variants. in future, we plan to design more effective label functions or employ more reliable weakly supervised learning approaches @xcite to further improve the performance. moreover, we will also introduce concept prerequisite relations into curriculum planning and intelligent tutoring applications, e.g. organizing learning resources into a reasonable order and incorporating prerequisite relations into knowledge tracing technologies.