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.

翻译：减少尺寸对于探索性数据分析是有用的。在许多应用中,发现与“背景”数据集相对的“前景”数据集所丰富的变异是值得注意的。最近,为这一环境提出了对比性主要组成部分分析(CPCA),但由于缺乏正式的概率模型,很难理解CPCA并调和其超参数。在这项工作中,我们提出了一种以模型为基础的替代CPCA的概率对比性主要组成部分分析(PCPCA)。我们讨论如何在理论和实践中设置超参数,我们展示了五氯苯酚对CPCA的一些优势,包括更大的可解释性、不确定性量化和有原则的推论、噪音的稳健性和缺失的数据,以及从模型中生成数据的能力。我们通过一系列基因表达、蛋白质表达和图像数据集的模拟和案例控制实验,展示了五氯苯酚的性能。