  Cognitive modeling commonly relies on asking participants to complete a
battery of varied tests in order to estimate attention, working memory, and
other latent variables. In many cases, these tests result in highly variable
observation models. A near-ubiquitous approach is to repeat many observations
for each test, resulting in a distribution over the outcomes from each test
given to each subject. In this paper, we explore the usage of latent variable
modeling to enable learning across many correlated variables simultaneously. We
extend latent variable models (LVMs) to the setting where observed data for
each subject are a series of observations from many different distributions,
rather than simple vectors to be reconstructed. By embedding test battery
results for individuals in a latent space that is trained jointly across a
population, we are able to leverage correlations both between tests for a
single participant and between multiple participants. We then propose an active
learning framework that leverages this model to conduct more efficient
cognitive test batteries. We validate our approach by demonstrating with
real-time data acquisition that it performs comparably to conventional methods
in making item-level predictions with fewer test items.
