Knowledge Tracing with Variational Lower-Bound Approximation
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Solution Overview
Problem
Existing knowledge tracing systems lack explainability and reliability in real-time predictions, particularly when dealing with limited data, making it difficult for instructors to understand the reasoning behind AI predictions and ensuring the accuracy of those predictions.
Innovation Solution
A knowledge tracing device and method that utilizes a variational parameter determination unit, gradient direction lower bound calculation, and full dimensional lower bound calculation to enhance the explainability and reliability of prediction results by approximating likelihood functions with Gaussian distributions, even in real-time scenarios.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If deep learning methods are used for real-time knowledge tracing, then prediction speed is improved, but explainability of prediction reasons deteriorates
Solution Approach 1:
The patent introduces an intermediary mechanism that bridges deep learning predictions and explainable outputs. By using variational inference to approximate the posterior distribution of student knowledge states, the system maintains the speed of deep learning while generating interpretable predictions about what the student knows and doesn't know, thus preserving explainability information that would otherwise be lost in black-box deep learning models.
2Productivity
If knowledge tracing is performed with limited learner data, then real-time processing is maintained, but reliability of prediction results deteriorates
Solution Approach 1:
The patent applies prior cushioning by incorporating prior distributions over student knowledge states before observing actual learner data. This allows the system to provide reliable predictions even when learner data is limited, as the prior distribution acts as a cushion that prevents unreliable predictions. The variational inference framework combines these priors with observed data to produce robust predictions in real-time.
3Measurement precision
If complex models incorporating prerequisite relations are used, then measurement precision of knowledge state is improved, but device complexity deteriorates
Solution Approach 1:
The patent transforms the complex model structure into a more manageable form by changing parameters through variational inference. Instead of directly modeling complex prerequisite relations in a black-box deep learning model, the system uses variational parameters to represent student knowledge states, which can be efficiently updated and interpreted. This parameter transformation maintains measurement precision while reducing the effective complexity of the model.
Data Source
AI summary
The variational parameter determination unit 81 determines a variational parameter that specifies a position where a likelihood function and a lower bound of the likelihood function to be approximated by Gaussian are in contact. The gradient direction lower bound calculation unit 82 generates a likelihood function made one-dimensional in a gradient direction at the center of a prior distribution and calculates the lower bound of the generated likelihood function. The full dimensional lower bound calculation unit 83 sets covariances in directions other than the gradient direction to an arbitrary covariance and calculates the lower bounds of the set covariances.