Structure Learning of Latent Factors via Clique Search on Correlation Thresholded Graphs

TL;DR

This paper introduces a fast correlation thresholding algorithm that learns the number of latent factors and the model structure in factor analysis, with theoretical guarantees and scalability to high-dimensional data.

Contribution

The paper proposes a novel clique search-based method that simultaneously determines the number of factors and identifies a rotationally identifiable structure, overcoming key limitations of existing methods.

Findings

The CT algorithm accurately recovers factor structures in simulations.

It scales efficiently to thousands of variables.

The method is robust to assumption violations.

Abstract

Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.