A Dual Formulation for Probabilistic Principal Component Analysis

Abstract

In this paper, we characterize Probabilistic Principal Component Analysis in Hilbert spaces and demonstrate how the optimal solution admits a representation in dual space. This allows us to develop a generative framework for kernel methods. Furthermore, we show how it englobes Kernel Principal Component Analysis and illustrate its working on a toy and a real dataset.

ICML 2023 Workshop on Duality for Modern Machine Learning (DP4ML). 14 pages (8 main + 5 appendix), 4 figures and 4 tables