(3/5) Multi-output Gaussian Processes: principal component analysis, Karhunen-Loeve eigenfunctions

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 09:46

Summary:

This video presents the PCA (principal component analysis) of the covariance matrix (at a finite set of points) of a 2-output gaussian process whose motivation and covariance structure details were discussed in previous videos [mimoGP1EN] and [mimogp2EN]. When the number of points is infinity, in the continuous-input case principal components are Karhunen-Loeve (KL) eigenfunctions. See bottom note for references to one-output KL analysis.

In here, we exploit the special structure of 2-output Gaussian process to better understand such eigenfunctions via suitable plots, seeing that some eigenfunctions are equal in both outputs (strong common component) and only at higher frequencies eigenfunctions appear explaining the difference between the two outputs.

A simpler single-output Gaussian process PCA (KL) is studied in videos [gpkh2EN] and [gpkh2pEN].

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.