UC San Diego

Biomedical data sets are rapidly growing in size and complexity due to advances in data collection technologies, including the widespread adoption of DNA and RNA sequencing. Beyond their high dimensionality, these datasets often exhibit intricate correlation structures across multiple, interconnected levels. In cancer genomics, for example, transcriptomic, mutational, epigenetic, and other types of ‘omics data are now collected not only at the bulk sample level but increasingly at single-cell resolution. This complexity underscores the need for robust methodologies that can extract biological meaning while addressing challenges of computational scalability and high dimensionality.To address these challenges, I first developed the Multi-Scale Copula Entropy (MCI) metric, an information-theoretic measure of correlation that is both robust and sensitive. MCI accurately quantifies associations in linear and non-linear relationships while remaining computationally efficient. Second, I introduced a variable sparsity-constrained Non-Negative Matrix Factorization (vsNMF) method, where the sparsity of individual components can be tuned as a hyperparameter. This enables the extraction of patterns at different levels of granularity from input data matrices. I demonstrate how it can be used within the Cancer States and Archetypes (CSA) framework to model state changes both in-vitro, under pharmaceutical and genetic perturbations in cell lines, and in-vivo, under clinical pharmaceutical exposures. Finally, I generalized vsNMF to higher-dimensional tensor decomposition, creating a variable sparsity non-negative Tucker decomposition algorithm. I applied this method to a published single-cell RNA sequencing dataset from COVID-19 patients, paired with clinical response information, and successfully recapitulated findings linking cytokine storms to clinical outcomes.