This dissertation aims to develop a latent variable modeling framework with which to analyze gene expression profiling data for computational dissection of molecular signatures and transcriptional modules. The first part of the dissertation is focused on extracting pure gene expression signals from tissue or cell mixtures. The main goal of gene expression profiling is to identify the pure signatures of different cell types (such as cancer cells, stromal cells and inflammatory cells) and estimate the concentration of each cell type. In order to accomplish this, a new blind source separation method is developed, namely, nonnegative partially independent component analysis (nPICA), for tissue heterogeneity correction (THC). The THC problem is formulated as a constrained optimization problem and solved with a learning algorithm based on geometrical and statistical principles. The second part of the dissertation sought to identify gene modules from gene expression data to uncover important biological processes in different types of cells. A new gene clustering approach, nonnegative independent component analysis (nICA), is developed for gene module identification. The nICA approach is completed with an information-theoretic procedure for input sample selection and a novel stability analysis approach for proper dimension estimation. Experimental results showed that the gene modules identified by the nICA approach appear to be significantly enriched in functional annotations in terms of gene ontology (GO) categories. The third part of the dissertation moves from gene module level down to DNA sequence level to identify gene regulatory programs by integrating gene expression data and protein-DNA binding data. A sparse hidden component model is first developed for this problem, taking into account a well-known biological principle, i.e., a gene is most likely regulated by a few regulators. This is followed by the development of a novel computational approach, motif-guided sparse decomposition (mSD), in order to integrate the binding information and gene expression data. These computational approaches are primarily developed for analyzing high-throughput gene expression profiling data. Nevertheless, the proposed methods should be able to be extended to analyze other types of high-throughput data for biomedical research. / Ph. D.