Learning a Factor Model via Regularized PCA

TL;DR

This paper introduces a regularized PCA method for learning linear factor models, demonstrating improved accuracy over existing methods through experiments and theoretical analysis, with computational efficiency comparable to standard PCA.

Contribution

The paper presents a novel regularized PCA approach that corrects biases in traditional factor analysis while maintaining computational efficiency.

Findings

Regularized PCA outperforms existing factor analysis methods in experiments.

Theoretical results explain bias correction achieved by the new algorithm.

Algorithm maintains PCA-like computational efficiency.

Abstract

We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those produced by pre-existing factor analysis approaches. We also establish theoretical results that explain how our algorithm corrects the biases induced by conventional approaches. An important feature of our algorithm is that its computational requirements are similar to those of PCA, which enjoys wide use in large part due to its efficiency.