High-Dimensional Covariate-Augmented Overdispersed Poisson Factor Model

TL;DR

This paper introduces a covariate-augmented overdispersed Poisson factor model for high-dimensional count data, combining theoretical guarantees with a novel estimation scheme and demonstrating superior performance in simulations and real data.

Contribution

It proposes a new high-dimensional Poisson factor model that incorporates observable covariates and develops a variational estimation method with theoretical guarantees.

Findings

Outperforms existing methods in accuracy and efficiency

Provides theoretical identifiability conditions

Successfully applied to CITE-seq dataset

Abstract

The current Poisson factor models often assume that the factors are unknown, which overlooks the explanatory potential of certain observable covariates. This study focuses on high dimensional settings, where the number of the count response variables and/or covariates can diverge as the sample size increases. A covariate-augmented overdispersed Poisson factor model is proposed to jointly perform a high-dimensional Poisson factor analysis and estimate a large coefficient matrix for overdispersed count data. A group of identifiability conditions are provided to theoretically guarantee computational identifiability. We incorporate the interdependence of both response variables and covariates by imposing a low-rank constraint on the large coefficient matrix. To address the computation challenges posed by nonlinearity, two high-dimensional latent matrices, and the low-rank constraint, we propose a novel variational estimation scheme that combines Laplace and Taylor approximations. We also develop a criterion based on a singular value ratio to determine the number of factors and the rank of the coefficient matrix. Comprehensive simulation studies demonstrate that the proposed method outperforms the state-of-the-art methods in estimation accuracy and computational efficiency. The practical merit of our method is demonstrated by an application to the CITE-seq dataset. A flexible implementation of our proposed method is available in the R package \emph{COAP}.