High-throughput RNA sequencing technologies have transformed the study of cellular heterogeneity and dynamic gene expression programs. Bulk RNA sequencing provides aggregate measurements from mixed cell populations, whereas single-cell RNA sequencing offers cell-level resolution but is often affected by sparsity, technical noise, and limited sample coverage. These complementary characteristics motivate the development of statistical methods and computational algorithms that integrate bulk and single-cell transcriptomic data to estimate latent cellular compositions and characterize temporal gene expression dynamics. This dissertation develops two statistical learning frameworks for transcriptomic data analysis. The first framework, GSNMF+, addresses bulk RNA-seq deconvolution by incorporating single-cell reference information into a geometry-guided nonnegative matrix factorization model. Standard NMF-based deconvolution is often ill-posed and sensitive to initialization and noise in the data. To improve robustness and interpretability, GSNMF+ introduces augmented pseudo-bulk mixtures, a solvability-guided regularization term, and a manifold-based penalty to encourage biologically meaningful latent components and stable proportion estimates. Simulation studies with known ground-truth proportions demonstrate that GSNMF+ improves deconvolution accuracy compared with existing approaches. Real bulk RNA-seq applications further show that the method produces more consistent stage-composition estimates across independent single-cell reference datasets. The second framework, BetaDE, focuses on pseudotime-based differential expression analysis for single-cell RNA-seq data. Instead of relying on a single smooth trajectory model, BetaDE represents temporal gene expression patterns using a collection of beta-shaped basis functions that capture diverse activation patterns along pseudotime. To accommodate the distributional features of single-cell count data, including overdispersion and excess zeros, BetaDE considers multiple count-based models, including Poisson, Negative Binomial, zero-inflated Poisson, and zero-inflated Negative Binomial models. Model and kernel selection are performed using Akaike Information Criterion, followed by hypothesis testing to identify genes with significant temporal expression changes. The fitted kernel-based features are further used for functional clustering to recover groups of genes with similar dynamic expression patterns. Together, these two projects address complementary challenges in transcriptomic analysis: estimating hidden cellular compositions from bulk RNA-seq data and modeling dynamic gene expression programs from single-cell RNA-seq data. By combining matrix factorization, geometric regularization, data augmentation, pseudotime modeling, flexible count distributions, and functional clustering, this dissertation provides statistical tools for integrative analysis of bulk and single-cell RNA-seq data, with applications demonstrating their utility in complex biological systems.
