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Covariate-moderated Empirical Bayes Matrix Factorization.

William R P Denault1, Karl Tayeb1, Peter Carbonetto1

  • 1Departments of Statistics and Human Genetics, University of Chicago, Chicago, IL 60637, USA.

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This study introduces covariate-moderated empirical Bayes matrix factorization (cEBMF), a flexible framework for analyzing complex data. cEBMF effectively integrates diverse side information to improve matrix factorization, enhancing structure discovery in machine learning and statistics.

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Matrix factorization is key for uncovering structure in multivariate data.
  • Existing methods for incorporating side information are limited in data types and model flexibility.
  • Leveraging diverse side information can significantly improve matrix factorization performance.

Purpose of the Study:

  • Introduce a novel, flexible matrix factorization method.
  • Develop a framework that integrates arbitrary side information.
  • Improve the estimation of underlying data structures using side information.

Main Methods:

  • Introduce covariate-moderated empirical Bayes matrix factorization (cEBMF).
  • Design cEBMF as a modular framework accepting probabilistic models or neural networks for side information.
  • Utilize adaptive priors to accommodate different assumptions and constraints on factors.

Main Results:

  • Demonstrate the effectiveness of cEBMF through simulations.
  • Validate cEBMF on spatial transcriptomics data.
  • Showcase cEBMF's utility in collaborative filtering applications.

Conclusions:

  • cEBMF offers a versatile and powerful approach to matrix factorization.
  • The framework's modularity allows integration of diverse data types.
  • cEBMF enhances the discovery of latent structures in complex datasets.