LATENT VARIABLE MODELS FOR BINARY AND COUNT-VALUED DATA WITH APPLICATIONS TO SINGLE-CELL RNA-SEQUENCING DATA

In this dissertation we propose two latent variable models for binary and count-valued data. For the first proposed model we consider the problem of identifying stable sets of associated features in moderate or high-dimensional binary data. In this context we develop and investigate a method called Latent Association Mining for Binary data (LAMB). The LAMB method is based on a simple latent variable model in which the observed binary values represent a random thresholding of a latent continuous vector that may have a complex association structure. The model for the random thresholds is of limited complexity, but is flexible enough to capture meaningful associations in a dataset containing heterogeneity among samples or features or both. We consider a measure of latent association that quantifies association in the latent continuous vector without bias due to the random thresholding. The LAMB method uses an iterative testing based search procedure to identify stable sets of associated features. An important class of biological data is single-cell RNA-sequencing (scRNA-seq) data. A data matrix for scRNA-seq is high-dimensional, count-valued, and a majority of the observed counts are zero. Analyzing scRNA-seq data is a challenging problem because there is a low signal-to-noise ratio. We propose a latent variable model for scRNA-seq data, along with statistical methods to estimate the underlying mRNA expression of genes for a given data matrix. In contrast to related methods, the proposed method uses latent cell-cell correlations to account for important biological similarities in real scRNA-seq data. Meaningful estimates of true gene expression are produced by borrowing information across both cells and genes. We show that our estimates create a normalized scRNA-seq data matrix, and that downstream analysis methods can be applied to such normalized data. We compare the proposed method to related methods on artificial count-valued data and real scRNA-seq data.