동기: 그래프로 어떻게 exercise를 ?

1. ABSTRACT

   DKT

   • sort
     • Recurrent Neural Networks (RNNs)
     • Graph Neural Networks (GNNs)
   • drawbacks of former GNNs
   • more attentions paid on details of the nodes > high-level semantic information
   • struggle to effectively establish spatial associations and complex structures of the nodes
   • concepts or exercises - representation only, integration X
   • solution: Bi-Graph Contrastive Learning based Knowledge Tracing (Bi-CLKT)
     • self-supervised learning
     • a two-layer comparative learning scheme
     • based on an “exercise-to-exercise” (E2E) relational subgraph
     • joint contrastive loss (-> better representations, better prediction)
     • prediction layer: RNN vs memory-augmented neural networks

   “Model experiments conducted with four real-world datasets”

2. INTRODUCTION

   • Existing KT
     • target the “concept” to which the exercise belongs, not considering the cases that an exercise may correspond to multiple concepts, not considering the difficulty level
     • problem 1: not distinguishing between the exercises
     • solution 1: use exercise features as a supplement to concept input
     • problem 2: problems of sparse data (each student may only interact with a very small fraction of the exercises)
     • problem 3: might loses potential inter-exercise and inter-concept information
     • solution 3: “exercise-to-exercise” (E2E) and “concept-to-concept” (C2C) -> usage of graphs
   • GKT
     • widespread deployment of GNNs -> crossconcept exercises
   • Self-supervised learning
     • efficient
     • still in infancy compare to the domains of textual and image datasets

3. RELATED WORK

   • KT
     • BKT
       • Hidden Markov Model, Bayesian rules, binary variable
       • additional variables: slip and guess probabilities, concept difficulty, student personalisation
     • traditional machine learning KT models
       • factor analysis models (e.g., item response theory (IRT), performance factor analysis (PFA))
     • Deep Knowledge Tracing
       • effective in learning valid representations, large amounts of data
       • RNNs: track students’ knowledge states
       • DKVMN (Dynamic Key-Value Memory Network): dynamic matrix to store and update all concepts, dynamic matrix to store and update students’ learning states
       • deep matrix factorization method: conceptual representation, multi-view data
     • DKT considering exercises
       • EERNNA (Exercise-Enhanced Recurrent Neural Network with attention mechanism): text of the exercise -> embedding. But difficult to collect textual information, too much interference into the embedding
       • DSCMIN (Dynamic Student Classification on Memory Networks): problem difficulty
       • DHKT: using relationships between problems (exercise) and skills (concepts), but data sparsity issues
       • SKVMN (Sequence Key Value Memory Network): improved the LSTM to capture long-term dependencies
   • Self-supervised Learning and graph data
     • generative models
       • to learn the embedding of nodes of the graph into a latent space through GNN
       • reconstruct the structure and properties of the original graph
       • then learned representations encode the structural and attribute features of the original graph
     • contrastive models
       • global: augmented -> positive pair, other graphs -> negative pair
       • local: nodes are important. negative pairs exist even at the augmented graph
       • compare the loss functions to minimize the distance between positive pairs and maximize the distance between negative pairs
       • better for preventing overfitting

4. PRELIMINARY AND PROBLEM STATEMENT

   • Problem

     • Definition of student performance prediction problem: the accuracy with which students interact with the exercises under each concept (정답률?) -> the level of student mastery of each concept

   • Solution- Bi-CLKT summary

     • self-supervised learning
     • a two-layer comparative learning scheme
     • original “exercise-to-concept” (E2C) relations -> build the graph of exercise-influence relations
     • contrastive learning with global-bilayer and local-bilayer structures: learn the concepts and exercises separately
     • graph-level GCNs: extract “exercise-to-exercise” (E2E) relations
     • node-level GCNs**:** extract “concept-to-concept” (C2C) relations
     • the representation of exercise is combined by a joint contrastive loss function (-> better representations, better prediction)
     • students’ performance prediction: DNN prediction layer (RNN vs memory-augmented neural networks)

   • Solution - Bi-CLKT

     • normal: global or local

     • this: both -> Bi-graph -> node level GCN to learn “exercise-to-exercise” (E2E) embedding, graph-level GCN to learn “concept-to-concept” (C2C) embedding

     • specially, “exercise-to-exercise”(E2E) relationships extracted by students’ transitions between exercises

       • ‘Students who get two different exercises correct at the same time -> will have a high degree of similarity between the two exercises -> and therefore will have relatively high weights between them, and vice versa.’

     • construct an “exercise influence” graph

   • can solve the problems of exercises on first seen concepts, exercises involving multiple concepts

     • nodes connecting different exercises to each other
     • subgraphs connecting different concepts to each other

   • separate graph data augmentation of E2E and C2C, and logical elimination using PageRank (😀)

   • encoding: embed node level, graph level

   • metric embedding (projection head): apply graph-level and node-level GCNs at the graph (using both E2E and C2C is the 😀)

   • contrast learning-based Knowledge Tracing graph

   • students’ performance prediction: RNN (😀) vs memory-augmented NN

   • DATA: accurate labels, practice and conceptual clarity, online tutoring site, rich number of records per student, interactions between |S| and C

• marks

1. Discussion