  The issue of missing data poses a great challenge on boosting performance and
application of deep learning models in the {\em Knowledge Tracing} (KT)
problem. However, there has been the lack of understanding on the issue in the
literature. %are not sufficient studies tackling this problem. In this work, to
address this challenge, we adopt a subject-based training method to split and
impute data by student IDs instead of row number splitting which we call
non-subject based training. The benefit of subject-based training can retain
the complete sequence for each student and hence achieve efficient training.
Further, we leverage two existing deep generative frameworks, namely
variational Autoencoders (VAE) and Longitudinal Variational Autoencoders (LVAE)
frameworks and build LSTM kernels into them to form LSTM-VAE and LSTM LVAE
(noted as VAE and LVAE for simplicity) models to generate quality data. In
LVAE, a Gaussian Process (GP) model is trained to disentangle the correlation
between the subject (i.e., student) descriptor information (e.g., age, gender)
and the latent space. The paper finally compare the model performance between
training the original data and training the data imputed with generated data
from non-subject based model VAE-NS and subject-based training models (i.e.,
VAE and LVAE). We demonstrate that the generated data from LSTM-VAE and
LSTM-LVAE can boost the original model performance by about 50%. Moreover, the
original model just needs 10% more student data to surpass the original
performance if the prediction model is small and 50\% more data if the
prediction model is large with our proposed frameworks.
