High-probability bounds for the reconstruction error of PCA

TL;DR

This paper derives probabilistic bounds on PCA reconstruction error in infinite-dimensional spaces, with applications to covariance operators with polynomial or exponential eigenvalue decay.

Contribution

It provides new high-probability bounds for PCA reconstruction error applicable to infinite-dimensional settings with specific eigenvalue decay conditions.

Findings

High-probability bounds for PCA error in infinite dimensions

Application to covariance operators with polynomial eigenvalue decay

Application to covariance operators with exponential eigenvalue decay

Abstract

We derive high-probability bounds for the reconstruction error of PCA in infinite dimensions. We apply our bounds in the case that the eigenvalues of the covariance operator satisfy polynomial or exponential upper bounds.