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Archive / INF Seminars / INF_2024_12_06_HeleneRuffieux

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	A Bayesian functional factor model for high-dimensional curves

Host: Prof. Deborah Sulem

Friday

06.12

USI East Campus, Room D5.01

11:00 - 12:00


	Hélène Ruffieux University of Cambridge

Abstract: The increasing availability of longitudinal measurements is set to yield important scientific discoveries in domains such as healthcare, medicine, economics and social sciences. While functional data analysis is an active area of research, methods for modelling complex multivariate functional dependencies remain limited. Motivated by a COVID-19 study conducted at Addenbrooke’s and Papworth Hospitals in Cambridge, which will serve as an illustrative thread throughout this talk, 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. We develop a variational inference algorithm, with analytical updates, that couples efficiency and principled parameter uncertainty quantification, and we introduce a model selection procedure for learning the number of factors. Extensive numerical experiments illustrate the ability of the approach to (i) accurately estimate variable-specific loadings, FPCA latent functions and subject-specific component scores, and (ii) scale to high-dimensional datasets (e.g., with panels of 20,000 genes measured longitudinally for 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, pointing to key biological pathways, and further enables prediction of molecular trajectories at the subject level, towards targeted interventions and personalised treatments.

This is joint work with Salima Jaoua and Daniel Temko.

Biography: Hélène Ruffieux is a Senior Research Fellow at the MRC Biostatistics Unit of the University of Cambridge. She holds a PhD in Mathematics from EPFL. Her research concerns the development of Bayesian methods and their application to open problems in biomedicine, with a focus on scalable hierarchical modelling approaches for variable selection, latent structure discovery and network estimation, in high-dimensional or temporal data settings.

Seminar can be joined online by clicking here.