Cross-Validation for Unsupervised Learning

TL;DR

This paper explores extending cross-validation techniques to unsupervised learning, particularly for selecting the number of principal components, demonstrating its effectiveness through simulations and theoretical analysis.

Contribution

It introduces a latent factor model and an objective criterion for applying cross-validation to estimate data dimensionality in unsupervised learning.

Findings

Cross-validation can effectively estimate the number of principal components.

Simulation results support CV's utility in unsupervised model selection.

Theoretical analysis confirms the validity of the proposed approach.

Abstract

Cross-validation (CV) is a popular method for model-selection. Unfortunately, it is not immediately obvious how to apply CV to unsupervised or exploratory contexts. This thesis discusses some extensions of cross-validation to unsupervised learning, specifically focusing on the problem of choosing how many principal components to keep. We introduce the latent factor model, define an objective criterion, and show how CV can be used to estimate the intrinsic dimensionality of a data set. Through both simulation and theory, we demonstrate that cross-validation is a valuable tool for unsupervised learning.