Knowledge tracing device, method, and program
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.
1 . A knowledge tracing device comprising:
one or more memories storing instructions; and
one or more processors configured to execute the instructions to:
determine a variational parameter that specifies a position where a likelihood function representing a non-compensation model for educational skill assessment and a lower bound of the likelihood function to be approximated by Gaussian are in contact;
generate a likelihood function made one-dimensional in a gradient direction at the center of a prior distribution representing learner skill states and calculates the lower bound of the generated likelihood function using quadratic approximation for real-time processing; and
set covariances in directions other than the gradient direction to an arbitrary covariance and calculates the lower bounds of the set covariances to enable reliable educational decision-making.
2 . The knowledge tracing device according to claim 1 , wherein the processor further executes instructions to set the covariances in directions other than the gradient direction to the variance of a prior distribution.
3 . The knowledge tracing device according to claim 1 , wherein the processor further executes instructions to determine a position where likelihood exceeds a predetermined threshold or a position obtained by optimizing differentiation of marginal likelihood, as the variational parameter.
4 . The knowledge tracing device according to claim 1 , wherein the likelihood function is represented as a product of functions that represent skills required by a learner to solve a problem.
5 . The knowledge tracing device according to claim 1 , wherein the processor further executes instructions to generate an a-message in the Kalman filter by multiplying the lower bound of the calculated likelihood function with the prior distribution.
6 . The knowledge tracing device according to claim 5 , wherein the processor further executes instructions to generate the a-message using a state transition model in which a bias term representing a feature of a learner is included in a mean of a Gaussian distribution.
7 . A knowledge tracing method implemented by a computer, the method comprising:
determining a variational parameter that specifies a position where a likelihood function representing a non-compensation model for educational skill assessment and a lower bound of the likelihood function to be approximated by Gaussian are in contact;
generating a likelihood function made one-dimensional in a gradient direction at the center of a prior distribution representing learner skill states and calculating the lower bound of the generated likelihood function using quadratic approximation for real-time processing; and
setting covariances in directions other than the gradient direction to an arbitrary covariance and calculating the lower bounds of the set covariances to enable reliable educational decision-making.
8 . The knowledge tracing method according to claim 7 , wherein the computer sets the covariances in directions other than the gradient direction to the variance of a prior distribution.
9 . A non-transitory computer readable information recording medium storing a knowledge tracing program, which when executed by a processor, that performs operations comprising:
determining a variational parameter that specifies a position where a likelihood function representing a non-compensation model for educational skill assessment and a lower bound of the likelihood function to be approximated by Gaussian are in contact;
generating a likelihood function made one-dimensional in a gradient direction at the center of a prior distribution representing learner skill states and calculating the lower bound of the generated likelihood function using quadratic approximation for real-time processing; and
setting covariances in directions other than the gradient direction to an arbitrary covariance and calculating the lower bounds of the set covariances to enable reliable educational decision-making.
10 . The non-transitory computer readable information recording medium according to claim 9 , further comprising:
setting the covariances in directions other than the gradient direction to the variance of a prior distribution.