A0732
Title: Probabilistic contrastive principal component analysis
Authors: Didong Li - University of North Carolina at Chapel Hill (United States) [presenting]
Andy Jones - Princeton University (United States)
Barbara Engelhardt - Princeton University (United States)
Abstract: Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover a variation that is enriched in a ``foreground'' dataset relative to a ``background'' dataset. Recently, contrastive principal component analysis (CPCA) was proposed for this setting. However, the lack of a formal probabilistic model makes it difficult to reason about CPCA and tune its hyperparameter. We propose probabilistic contrastive principal component analysis (PCPCA), a model-based alternative to CPCA. We discuss how to set the hyperparameter in theory and in practice, and we show several of PCPCA's advantages over CPCA, including greater interpretability, uncertainty quantification and principled inference, robustness to noise and missing data, and the ability to generate data from the model. We demonstrate PCPCA's performance through a series of simulations and case-control experiments with datasets of gene expression, protein expression, and images.
