A Dual Formulation for Probabilistic Principal Component Analysis

Abstract

TL;DR: We give a dual equivalent of Probabilistic PCA, which work with kernels.

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.

Acknowlegdements

EU: The research leading to these results has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation program / ERC Advanced Grant E-DUALITY (787960). This paper reflects only the authors’ views and the Union is not liable for any use that may be made of the contained information. Research Council KUL: Optimization frameworks for deep kernel machines C14/18/068. Flemish Government: FWO: projects: GOA4917N (Deep Restricted Kernel Machines: Methods and Foundations), PhD/Postdoc grant; This research received funding from the Flemish Government (AI Research Program). All the authors are also affiliated to Leuven.AI - KU Leuven institute for AI, B-3000, Leuven, Belgium.