# A Dual Formulation for Probabilistic Principal Component Analysis

arXiv: https://arxiv.org/abs/2307.10078 · HTML: https://mlsanity.com/paper/2307.10078/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 19 Jul 2023.

## Builds on (most cited first, 5 of 5)

- [Disentangled Representation Learning and Generation with Manifold Optimization](https://mlsanity.com/paper/2006.07046/) (2020)
- [Convex Formulation for Kernel PCA and its Use in Semi-Supervised Learning](https://mlsanity.com/paper/1610.06811/) (2016)
- [Generative Restricted Kernel Machines: A Framework for Multi-view Generation and Disentangled Feature Learning](https://mlsanity.com/paper/1906.08144/) (2019)
- [Robust Generative Restricted Kernel Machines using Weighted Conjugate Feature Duality](https://mlsanity.com/paper/2002.01180/) (2020)
- [Latent Space Exploration Using Generative Kernel PCA](https://mlsanity.com/paper/2105.13949/) (2021)

## Abstract (arXiv)

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.