Probabilistically-autoencoded horseshoe-disentangled multidomain item-response theory models*

Item response theory (IRT) is a non-linear generative probabilistic paradigm for using exams in order to quantify latent traits. In multidimensional IRT, one requires a factorization of the test items. For this task, linear factor analysis methods are often used, making IRT a posthoc model. We propose skipping the initial factor analysis by using a sparsity-promoting horseshoe prior to perform factorization directly within the IRT model so that all training occurs in a single self-consistent step. By binding the generative IRT model to a Bayesian neural network (forming a probabilistic autoencoder), one obtains a scoring algorithm consistent with the interpretable Bayesian model. In some IRT applications the black-box nature of a neural network scoring machine is desirable. Within this problem, we investigate the translation of some regularization principles common in Bayesian modeling to neural networks.