Hélène Ruffieux (MRC Biostatistics Unit, University of Cambridge) – A Bayesian functional factor model for high-dimensional curves

The increasing availability of longitudinal data is set to yield scientific discoveries across various domains, yet methods for modelling complex multivariate functional dependencies remain limited.

Motivated by a COVID-19 study conducted in Cambridge hospitals, we propose a Bayesian approach for representing high-dimensional curves, combining latent factor modelling and functional principal component analysis (FPCA). This approach captures correlations across variables (e.g., biomarkers) and time, by positing that subsets of variables contribute to a small number of FPCA expansions (e.g., representing latent disease processes) through variable-specific loadings. Subject variability is modelled using a small number of functional principal components, each characterised by a smoothly varying temporal function. A variational inference algorithm with simulated annealing ensures efficient exploration of multimodal distributions.

Our numerical experiments demonstrate reliable parameter estimation and scalability to high-dimensional data (such as longitudinal measurements of 20,000 genes across a few hundred subjects). Through the COVID-19 study, we illustrate how our framework helps disentangle disease heterogeneity. It clarifies which biomarkers coordinate over time and predicts molecular trajectories at the subject level, towards personalised treatment strategies.

This is joint work with Salima Jaoua and Daniel Temko.