Mixtures of Latent Variable Models for Interpreting Gene Expression Covariation from Pathways to Transcriptomes

This thesis centers on interpretable subspace learning and latent variable models for characterizing covariation modulated by categorical variables in the context of biology. First, it introduces a probabilistic model with ties to Principal Component Analysis and k-means clustering, k-spaces, which has implications across different biological analyses through its interpretations as a subspace learning technique, a latent variable model, and a dimension reduction technique. Second, it establishes the problem of simultaneously characterizing gene covariation and expression level in known pathways in human tissue samples and applies k-spaces to GTEx data to lay the foundations for this line of research. Finally, it outlines a path forward to being able to use such data as references for clinical samples from patients.