Bayesian Non-Parametric Factor Analysis for Longitudinal Spatial Surfaces: An Application in Glaucoma

Seminar Series

Friday, March 5, 2021 - 02:00
Zoom Conference
Samuel Berchuck, PhD

Abstract: Factor analysis is a statistical technique for modeling multivariate data as a function of a small number of underlying factors. In standard factor analysis, this dimension reduction is performed without respect to any dependencies in the data. When the multivariate response is a spatial surface this assumption is no longer appropriate, and an adaptation is required. We introduce a Bayesian non-parametric spatial factor analysis model with spatial dependency induced through a prior on factor loadings. For each column of the loadings matrix, spatial dependency is encoded using a probit stick-breaking process (PSBP) and a multiplicative gamma process shrinkage prior is used across columns to adaptively determine the number of latent factors. By encoding spatial information into the loadings matrix, meaningful factors are learned that respect the observed neighborhood dependencies, making them useful for assessing rates over space. Furthermore, the spatial PSBP prior can be used for clustering temporal trends, allowing users to identify regions within the spatial domain with similar temporal trajectories, an important task in many applied settings. In this talk, we will illustrate the model’s performance in the context of glaucoma, applying the introduced method to longitudinal series of visual fields to identify glaucoma disease progression. The R package spBFA, available on CRAN, implements the method.

Bio: Dr. Berchuck is a postdoc in the Department of Statistical Science at Duke University, and a Forge Scholar in Duke Forge, Duke’s Center for Actionable Health Data Science. He received his PhD from the Department of Biostatistics from the Gillings School of Global Public Health at the University of North Carolina at Chapel Hill. Dr. Berchuck’s research focuses heavily on the development of interpretable and computationally efficient spatiotemporal Bayesian hierarchical models and machine learning algorithms for high-dimensional data settings across medicine and public health, including medical imaging and electronic health records. His applied contributions have largely been in the field of glaucoma, where methods are developed to efficiently detect functional disease progression from longitudinal series of visual fields. He has received various awards for his work, including recently receiving recognition from RStudio for his published R packages.


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