Vine Copulas in Machine Learning

The availability of high-quality data and the reliable quantification of uncertainty about conclusions drawn from that data, are two key factors for scientific progress in biomedical research and for clinical decision making. However, privacy concerns about patient-level data prohibit (easy) sharing of data. This hinders broad research collaborations, the re-production of existing study results and the data serving as benchmarks for methodological developments in bio-statistics and machine learning (ML), and thus slows down research progress in bio-statistics and ML, and in medicine in general. In medical research and practice, it is ultimately patients’ well-being and lives that are at stake. Therefore, research findings cannot be ethically applied to clinical practice and decision making, if they are not accompanied by appropriate quantification of uncertainty that can be taken into account. However, uncertainty quantification can be computationally costly, hindering its application in biomedical research.
ML is a toolbox with solutions to both of these challenges. Private generative modeling produces synthetic data based on the sensitive real data. The synthetic data can be published and used in place of the real data, contributing to preserving individuals’ privacy. Variational inference efficiently approximates and quantifies uncertainty in complex settings. Depending on the choice of approximate posterior, complex unobserved dependencies can be modeled at a moderate computational cost. Vine copulas are a statistical model that flexibly models complex dependence in a fine-grained fashion and has been widely applied in medical research.
This thesis develops vine copula based methods for ML, namely for private generative modeling for synthetic data generation, and variational inference for uncertainty quantification. More specifically, the structure of vine copulas is exploited to balance privacy and utility in synthetic data generation in the first part, and to guide the flexibility in the uncertainty estimate in the second part.