Computational methods for heterogeneity, fairness and data quality with applications to biomedical data

Large-scale biomedical datasets present three interconnected challenges. Heterogeneity, which arises from diversity in biological systems, populations, and measurement conditions, obscures meaningful patterns. Fairness concerns the equitable treatment of demographic groups across the data collection to model prediction pipeline. Data quality reflects the accuracy, consistency, and reliability of recorded information, where errors undermine downstream inference. This dissertation develops computational methods to address each, with a focus on biomedical applications. Heterogeneity manifests in two ways. To address distortion caused by orthogonal outliers in multidimensional scaling, we introduce DeCOr-MDS, using n-simplex geometry to detect outliers, estimate intrinsic dimensionality, and correct pairwise distances. To address the inadequacy of Euclidean distances for shape-based analysis, we investigate whether the Square Root Velocity metric yields more faithful representations of cancer cell morphology. Fairness raises challenges at both the cross-population and model evaluation levels. To address distributional shift across populations in Electronic Health Records, we introduce OTTEHR, an optimal transport-based framework that aligns target patient embeddings to a source domain without requiring target labels and identifies inter-group treatment disparities. To address the lack of fairness testing for regression models, we define the Wasserstein projection distance as the minimal transport cost to achieve fairness and derive a hypothesis testing framework and data perturbation procedure. Longitudinal health surveys suffer from data quality issues, as self-reported onset ages often conflict across survey waves. We propose a reliability score-based stratification that prioritizes more trustworthy reports and a Bayesian adjustment that reconciles conflicts by treating each report as a noisy observation of a latent true onset age. Together, these contributions demonstrate that computational methods provide principled solutions to core challenges in biomedical data analysis.