Open Access
March 2022 Heterogeneous Large Datasets Integration Using Bayesian Factor Regression
Alejandra Avalos-Pacheco, David Rossell, Richard S. Savage
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Bayesian Anal. 17(1): 33-66 (March 2022). DOI: 10.1214/20-BA1240


Two key challenges in modern statistical applications are the large amount of information recorded per individual, and that such data are often not collected all at once but in batches. These batch effects can be complex, causing distortions in both mean and variance. We propose a novel sparse latent factor regression model to integrate such heterogeneous data. The model provides a tool for data exploration via dimensionality reduction and sparse low-rank covariance estimation while correcting for a range of batch effects. We study the use of several sparse priors (local and non-local) to learn the dimension of the latent factors. We provide a flexible methodology for sparse factor regression which is not limited to data with batch effects. Our model is fitted in a deterministic fashion by means of an EM algorithm for which we derive closed-form updates, contributing a novel scalable algorithm for non-local priors of interest beyond the immediate scope of this paper. We present several examples, with a focus on bioinformatics applications. Our results show an increase in the accuracy of the dimensionality reduction, with non-local priors substantially improving the reconstruction of factor cardinality. The results of our analyses illustrate how failing to properly account for batch effects can result in unreliable inference. Our model provides a novel approach to latent factor regression that balances sparsity with sensitivity in scenarios both with and without batch effects and is highly computationally efficient.


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Alejandra Avalos-Pacheco. David Rossell. Richard S. Savage. "Heterogeneous Large Datasets Integration Using Bayesian Factor Regression." Bayesian Anal. 17 (1) 33 - 66, March 2022.


Published: March 2022
First available in Project Euclid: 15 September 2020

MathSciNet: MR4377136
Digital Object Identifier: 10.1214/20-BA1240

Primary: 62-07 , 62F15
Secondary: 62P10

Keywords: Bayesian factor analysis , EM , Non-local priors , shrinkage

Vol.17 • No. 1 • March 2022
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