Probabilistic Contrastive Principal Component Analysis

Abstract

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, including greater interpretability, uncertainty quantification, 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 experiments with datasets of gene expression, protein expression, and images.

Isolating salient variations of interest in single-cell data with contrastiveVI

“…Isolating salient variations present only in a target dataset is the subject of contrastive analysis (CA) [56,3,22,29,40,2,48]. While many recent studies have modeled scRNAseq data by fitting probabilistic models and representing the data in a lower dimension [30,38,18,32,31], few of these models are designed for CA.…”

“…Isolating the variations enriched in a target dataset is the subject of contrastive analysis (CA) [5, 6, 7, 8, 9, 10]. Many recent studies proposed probabilistic latent variable models for analyzing single-cell data [11, 12, 13].…”

“…For example, data from healthy controls versus a diseased population or from pre-versus post-intervention groups form intuitive background and target pairs. Moreover, with the development of new technologies for measuring cellular responses to large numbers of perturbations in parallel, such as Perturb-Seq [11], MIX-Seq [35], MULTI-Seq [36], and sci-Plex [41] among others, tools for better understanding variations unique to such perturbed cells compared to control populations will be critical.Isolating salient variations present only in a target dataset is the subject of contrastive analysis (CA) [56,3,22,29,40,2,48]. While many recent studies have modeled scRNAseq data by fitting probabilistic models and representing the data in a lower dimension [30,38,18,32,31], few of these models are designed for CA.…”

A Novel Leak Detection Approach in Water Distribution Networks

“…The idea behind leak detection water distribution systems is to maintain disinfection levels, pressure and reduce water loss are equally important. To address the leak detection purposes, several approaches have been developed including principal component analysis (PCA) [1], [2], nonlinear PCA (NPCA) [3], Multi-Regional PCA (MRPCA) [4], probabilistic PCA (PPCA) [5], [6] and attribute PCA (APCA) [7]. However, most industrial systems are nonlinear.…”

Online statistical hypothesis test for leak detection in water distribution networks

“…To address the fault detection purposes, several approaches have been developed, including principal component analysis (PCA) [1][2][3], nonlinear PCA (NPCA) [4], Multi-Regional PCA (MRPCA) [5], probabilistic PCA (PPCA) [6], attribute PCA (APCA) [7] and interval PCA (IPCA) [8]. Other detection indices, including the Hotelling T 2 statistic [9], the sum of squared residuals SPE and the generalized likelihood ratio test (GLRT) have been used.…”