Probabilistic Contrastive Principal Component Analysis
This work provides a more principled and robust dimension reduction method for researchers needing to identify differential variation between datasets, addressing limitations of existing methods.
This paper introduces Probabilistic Contrastive Principal Component Analysis (PCPCA), a model-based alternative to the existing Contrastive Principal Component Analysis (CPCA) for discovering variation enriched in a foreground dataset relative to a background. PCPCA offers advantages such as greater interpretability, uncertainty quantification, robustness to noise and missing data, and the ability to generate data, demonstrated through simulations and case-control experiments on gene expression, protein expression, and image datasets.
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover 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 to tune its hyperparameter. In this work, 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.