UCLA

This dissertation develops and analyzes methods for interpretable and fair machine learning that account for stratified data. We investigate two settings in which data may exhibit meaningful differences across groups or sources. First, we propose and analyze Stratified Non-Negative Tensor Factorization, a tensor factorization method that incorporates stratum-level information while learning globally shared topics and stratum-dependent shifts. We develop an efficient multiplicative-update algorithm, incorporate total-variation regularization for image denoising, and demonstrate its effectiveness on synthetic and real-world datasets. Second, we investigate fairness in matrix completion via nuclear norm minimization. We show empirically that minority or structurally distinct groups can experience disproportionately higher reconstruction error under a globally shared low-rank model. We formalize statistical parity and equal opportunity for matrix completion and evaluate fairness-metric regularization and a group-aware formulation for addressing reconstruction disparities. Numerical experiments on synthetic and real datasets demonstrate the trade-offs between parity-based fairness and group-wise reconstruction accuracy. Together, these works demonstrate the value of accounting for local, group-specific structure alongside globally shared information, and develops approaches for incorporating this balance into matrix and tensor methods toward improved fairness and interpretability.