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High-dimensional covariate-augmented overdispersed poisson factor model.

Wei Liu1, Qingzhi Zhong2

  • 1School of Mathematics, Sichuan University, Chengdu 610041, China.

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|April 29, 2024
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Summary
This summary is machine-generated.

This study introduces a new Poisson factor model that incorporates observable covariates for high-dimensional count data. The covariate-augmented model improves estimation accuracy and computational efficiency, outperforming existing methods.

Keywords:
count datahigh-dimensional factor analysislow rankoverdispersionsingular value ratio

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Area of Science:

  • Statistics
  • Bioinformatics
  • Machine Learning

Background:

  • Traditional Poisson factor models often ignore observable covariates, limiting their explanatory power.
  • High-dimensional data settings, where variables and covariates increase with sample size, pose significant analytical challenges.

Purpose of the Study:

  • To propose a novel covariate-augmented overdispersed Poisson factor model for high-dimensional count data.
  • To jointly perform factor analysis and estimate large coefficient matrices, accounting for variable and covariate interdependence.
  • To develop a computationally efficient estimation scheme for complex, nonlinear models.

Main Methods:

  • A covariate-augmented overdispersed Poisson factor model is proposed.
  • Identifiability conditions are established for theoretical guarantees.
  • A variational estimation scheme combining Laplace and Taylor approximations is developed to handle nonlinearity and low-rank constraints.
  • A singular value ratio criterion is introduced for determining the number of factors and matrix rank.

Main Results:

  • The proposed method demonstrates superior estimation accuracy and computational efficiency compared to state-of-the-art techniques in simulations.
  • The model effectively incorporates interdependence between response variables and covariates through a low-rank constraint.
  • Successful application to a CITE-seq dataset highlights practical utility.

Conclusions:

  • The covariate-augmented Poisson factor model offers a powerful approach for high-dimensional count data analysis.
  • The developed variational estimation scheme provides an efficient solution for complex modeling challenges.
  • The R package COAP offers a flexible implementation for researchers.