  Statistical inference on the cancer-site specificities of collective
ultra-rare whole genome somatic mutations is an open problem. Traditional
statistical methods cannot handle whole-genome mutation data due to their
ultra-high-dimensionality and extreme data sparsity -- e.g., >30 million unique
variants are observed in the ~1700 whole-genome tumor dataset considered
herein, of which >99% variants are encountered only once. To harness
information in these rare variants we have recently proposed the "hidden genome
model", a formal multilevel multi-logistic model that mines information in
ultra-rare somatic variants to characterize tumor types. The model condenses
signals in rare variants through a hierarchical layer leveraging contexts of
individual mutations. The model is currently implemented using consistent,
scalable point estimation techniques that can handle 10s of millions of
variants detected across thousands of tumors. Our recent publications have
evidenced its impressive accuracy and attributability at scale. However,
principled statistical inference from the model is infeasible due to the
volume, correlation, and non-interpretability of the mutation contexts. In this
paper we propose a novel framework that leverages topic models from the field
of computational linguistics to induce an *interpretable dimension reduction*
of the mutation contexts used in the model. The proposed model is implemented
using an efficient MCMC algorithm that permits rigorous full Bayesian inference
at a scale that is orders of magnitude beyond the capability of out-of-the-box
high-dimensional multi-class regression methods and software. We employ our
model on the Pan Cancer Analysis of Whole Genomes (PCAWG) dataset, and our
results reveal interesting novel insights.
