Probabilistic Principal Component Analysis

Probabilistic Principal Component Analysis (PPCA) is a statistical method for dimensionality reduction that models data as a low-dimensional latent variable projected onto a higher-dimensional space, incorporating probabilistic assumptions to handle noise and uncertainty. Current research focuses on improving PPCA's estimation accuracy, particularly addressing identifiability issues and developing consistent estimators, as well as extending its capabilities through hybrid models like generative principal component regression and connections to other dimensionality reduction techniques such as variational autoencoders and kernel methods. These advancements enhance PPCA's applicability in diverse fields, including neuroscience, anomaly detection, and machine learning, by providing more robust and interpretable dimensionality reduction for complex datasets.