  We develop methods for reducing the dimensionality of large data sets, common
in biomedical applications. Learning about patients using genetic data often
includes more features than observations, which makes direct supervised
learning difficult. One method of reducing the feature space is to use latent
Dirichlet allocation to group genetic variants in an unsupervised manner.
Latent Dirichlet allocation describes a patient as a mixture of topics
corresponding to genetic variants. This can be generalized as a Bayesian tensor
decomposition to account for multiple feature variables. Our most significant
contributions are with hierarchical topic modeling. We design distinct methods
of incorporating hierarchical topic modeling, based on nested Chinese
restaurant processes and Pachinko Allocation Machine, into Bayesian tensor
decomposition. We apply these models to examine patients with one of four
common types of cancer (breast, lung, prostate, and colorectal) and siblings
with and without autism spectrum disorder. We linked the genes with their
biological pathways and combine this information into a tensor of patients,
counts of their genetic variants, and the genes' membership in pathways. We
find that our trained models outperform baseline models, with respect to
coherence, by up to 40%.
