High-Dimensional Overdispersed Generalized Factor Model With Application to Single-Cell Sequencing Data Analysis

Area of Science:

• Statistics
• Bioinformatics
• Genomics

Background:

• Current high-dimensional factor models inadequately handle mixed-type data and overdispersion.
• Overdispersion is common in biomedical and genomics data, posing analytical challenges.

Purpose of the Study:

• To propose an overdispersed generalized factor model (OverGFM) for high-dimensional nonlinear factor analysis on mixed-type data with overdispersion.
• To address computational challenges arising from nonlinear models with high-dimensional latent variables.

Main Methods:

• Developed an overdispersed generalized factor model (OverGFM) incorporating an additional error term for overdispersion.
• Proposed a novel variational Expectation-Maximization (EM) algorithm using Laplace and Taylor approximations for computational efficiency.
• Introduced a singular value ratio criterion for determining the optimal number of factors.

Main Results:

• The proposed variational EM algorithm demonstrates excellent convergence properties and provides explicit solutions.
• The singular value ratio criterion effectively determines the optimal number of factors.
• OverGFM significantly outperforms existing methods in estimation accuracy and computational efficiency through simulations.

Conclusions:

• OverGFM provides an effective solution for high-dimensional nonlinear factor analysis on overdispersed mixed-type data.
• The method shows practical utility in genomics applications and is available in the R package GFM.