residual Component Analysis: Generalizing PCA for more flexible inference in linear-Gaussian models

Introduction

Probabilistic principle component analysis (PPCA) decomposes the covariance of a data vector [math]\displaystyle{ y }[/math] in [math]\displaystyle{ R^p }[/math], into a low-rank term and a spherical noise term.

[math]\displaystyle{ y \sim N(0, WW^T+\sigma I ) }[/math]