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Bayesian group factor analysis with structured sparsity.

Shiwen Zhao1, Chuan Gao2, Sayan Mukherjee3

  • 1Computational Biology and Bioinformatics Program, Department of Statistical Science, Duke University, Durham, NC 27708, USA.

Journal of Machine Learning Research : JMLR
|September 25, 2025
PubMed
Summary
This summary is machine-generated.

We introduce a structured Bayesian group factor analysis model for analyzing multiple datasets. This method effectively recovers latent factors and handles high-dimensional data, enabling flexible regularization and scalable inference for complex biological and text data.

Keywords:
Bayesian structured sparsitycanonical correlation analysismixture modelsparameter expansionsparse and low-rank matrix decompositionsparse priors

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Area of Science:

  • Statistics
  • Machine Learning
  • Bioinformatics

Background:

  • Latent factor models are standard for analyzing low-dimensional linear structure in high-dimensional data.
  • Existing models often struggle with multiple coupled observation matrices and structured variance recovery.

Purpose of the Study:

  • To develop a structured Bayesian group factor analysis model extending traditional factor analysis to multiple observation matrices.
  • To enable unsupervised recovery of latent factors with element-wise and column-wise shrinkage.
  • To provide flexible regularization for both dense and sparse latent factors.

Main Methods:

  • Developed a structured Bayesian prior for the joint factor loading matrix, regularizing at three levels.
  • Employed fast parameter-expanded expectation-maximization for efficient parameter estimation.
  • Validated the model on simulated data and applied it to three high-dimensional real-world datasets.

Main Results:

  • The model successfully recovers sparse signals amidst dense effects in high-dimensional data.
  • Demonstrated scalability to a large number of observations.
  • Showcased flexible, factor-specific regularization for diverse sparsity levels and variance explained.
  • Achieved tractable inference suitable for genomic and text data.

Conclusions:

  • The structured Bayesian group factor analysis model offers a powerful and flexible approach for analyzing complex, high-dimensional datasets.
  • It enables robust recovery of latent structures and handles various data characteristics effectively.
  • The method is particularly well-suited for applications in bioinformatics and natural language processing.