Efficiently resolving rotational ambiguity in Bayesian matrix sampling with matching

TL;DR

This paper introduces a fast post-processing algorithm for Bayesian models with unidentifiable matrices, enabling reliable inference despite rotational ambiguity, and demonstrates its effectiveness through simulations and real data analysis.

Contribution

It proposes a novel, computationally efficient post-processing method combining Varimax orthogonalization and greedy matching for Bayesian matrix models with rotational ambiguity.

Findings

The method effectively resolves label and sign switching issues.

It outperforms existing methods in computational efficiency.

The algorithm is implemented in the infinitefactor R package.

Abstract

A wide class of Bayesian models involve unidentifiable random matrices that display rotational ambiguity, with the Gaussian factor model being a typical example. A rich variety of Markov chain Monte Carlo (MCMC) algorithms have been proposed for sampling the parameters of these models. However, without identifiability constraints, reliable posterior summaries of the parameters cannot be obtained directly from the MCMC output. As an alternative, we propose a computationally efficient post-processing algorithm that allows inference on non-identifiable parameters. We first orthogonalize the posterior samples using Varimax and then tackle label and sign switching with a greedy matching algorithm. We compare the performance and computational complexity with other methods using a simulation study and chemical exposures data. The algorithm implementation is available in the infinitefactor R package on CRAN.