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Uncertainty-aware Knowledge Tracing

Weihua Cheng, Hanwen Du, Chunxiao Li, Ersheng Ni, Liangdi Tan, Tianqi Xu, Yongxin Ni

TL;DR

Uncertainty-aware Knowledge Tracing (UKT) addresses the challenge of uncertain student interactions by modeling each interaction as a Gaussian distribution with a mean and covariance, capturing base knowledge and uncertainty. UKT introduces a Wasserstein-based self-attention mechanism to track transitions between distributional knowledge states using the $W_2$ distance, and augments learning with aleatory uncertainty-aware contrastive learning to resist random errors like careless mistakes or lucky guesses. The approach is validated on six real-world KT datasets, where UKT achieves superior AUC and accuracy compared with strong baselines and demonstrates robust handling of both epistemic and aleatory uncertainty. These results advance KT by integrating distributional representations with distribution-level attention and uncertainty-aware learning, offering practical benefits for personalized education on MOOC platforms.

Abstract

Knowledge Tracing (KT) is crucial in education assessment, which focuses on depicting students' learning states and assessing students' mastery of subjects. With the rise of modern online learning platforms, particularly massive open online courses (MOOCs), an abundance of interaction data has greatly advanced the development of the KT technology. Previous research commonly adopts deterministic representation to capture students' knowledge states, which neglects the uncertainty during student interactions and thus fails to model the true knowledge state in learning process. In light of this, we propose an Uncertainty-Aware Knowledge Tracing model (UKT) which employs stochastic distribution embeddings to represent the uncertainty in student interactions, with a Wasserstein self-attention mechanism designed to capture the transition of state distribution in student learning behaviors. Additionally, we introduce the aleatory uncertainty-aware contrastive learning loss, which strengthens the model's robustness towards different types of uncertainties. Extensive experiments on six real-world datasets demonstrate that UKT not only significantly surpasses existing deep learning-based models in KT prediction, but also shows unique advantages in handling the uncertainty of student interactions.

Uncertainty-aware Knowledge Tracing

TL;DR

Uncertainty-aware Knowledge Tracing (UKT) addresses the challenge of uncertain student interactions by modeling each interaction as a Gaussian distribution with a mean and covariance, capturing base knowledge and uncertainty. UKT introduces a Wasserstein-based self-attention mechanism to track transitions between distributional knowledge states using the distance, and augments learning with aleatory uncertainty-aware contrastive learning to resist random errors like careless mistakes or lucky guesses. The approach is validated on six real-world KT datasets, where UKT achieves superior AUC and accuracy compared with strong baselines and demonstrates robust handling of both epistemic and aleatory uncertainty. These results advance KT by integrating distributional representations with distribution-level attention and uncertainty-aware learning, offering practical benefits for personalized education on MOOC platforms.

Abstract

Knowledge Tracing (KT) is crucial in education assessment, which focuses on depicting students' learning states and assessing students' mastery of subjects. With the rise of modern online learning platforms, particularly massive open online courses (MOOCs), an abundance of interaction data has greatly advanced the development of the KT technology. Previous research commonly adopts deterministic representation to capture students' knowledge states, which neglects the uncertainty during student interactions and thus fails to model the true knowledge state in learning process. In light of this, we propose an Uncertainty-Aware Knowledge Tracing model (UKT) which employs stochastic distribution embeddings to represent the uncertainty in student interactions, with a Wasserstein self-attention mechanism designed to capture the transition of state distribution in student learning behaviors. Additionally, we introduce the aleatory uncertainty-aware contrastive learning loss, which strengthens the model's robustness towards different types of uncertainties. Extensive experiments on six real-world datasets demonstrate that UKT not only significantly surpasses existing deep learning-based models in KT prediction, but also shows unique advantages in handling the uncertainty of student interactions.
Paper Structure (27 sections, 8 equations, 6 figures, 4 tables)

This paper contains 27 sections, 8 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Deep Sequential Models
  4. Memory-Augmented Models
  5. Adversarial Learning-Based Models
  6. Graph-Based Models
  7. Attention-Based Models
  8. Preliminaries
  9. Uncertainty Definition
  10. Epistemic Uncertainty
  11. Aleatory Uncertainty
  12. Problem Statement
  13. Methodology
  14. Stochastic Embedding Layers
  15. Wasserstein-Based Self-Attention
  16. ...and 12 more sections

Figures (6)

  • Figure 1: The impact of uncertainty on knowledge state under deterministic and stochastic modeling.
  • Figure 2: The impact of aleatory uncertainty on knowledge state under stochastic modeling. KCs are the knowledge concepts involved in the given questions.
  • Figure 3: The differences between deterministic KT and UKT architectures.
  • Figure 4: AUC of UKT with varying $\lambda$ values.
  • Figure 5: The heatmap of the mean of the covariance matrix of sequences in a batch from the Algebra2005 dataset.
  • ...and 1 more figures