High-Dimensional Covariate-Augmented Overdispersed Poisson Factor Model
高维协变量增强的过度离散泊松因子模型AI 解读 ↓
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高维协变量增强的过度离散泊松因子模型
- 研究问题
- 在计数响应变量或协变量维度随样本量增长时，如何结合可观测协变量与潜在因子，刻画过度离散及变量间依赖？
- 方法与思路
- 作者提出协变量增强的泊松因子模型，对系数矩阵施加低秩约束，并结合拉普拉斯与泰勒近似构造变分估计方案。
- 材料陈述的贡献
- 摘要称提供可识别性条件及因子数、矩阵秩的选择准则，模拟显示估计与计算优势，并以 CITE-seq 数据展示应用。
- 阅读关注点
- 应核对可识别性约束如何区分协变量效应与潜在因子、变分近似误差，以及奇异值比准则和模拟比较的适用条件。
- 阅读边界
- 这是 arXiv 预印本，不能据此确认同行评审或期刊接收。摘要未说明具体识别条件、误差保证及性能优势的适用范围。
原文摘要
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}.