Data Thinning for Poisson Factor Models and its Applications
提出一种基于泊松分布稀疏性质的信息准则ICDT，用于确定泊松因子模型中的因子数量，无需先验知识，并在回归中扩展了降维应用。
The Poisson factor model is a powerful tool for dimension reduction and visualization of large-scale count datasets across diverse domains. Despite the availability of efficient algorithms for estimating factors and loadings, existing methods either require prior knowledge of the number of factors, or resort to ad hoc criteria for its determination. This article proposes a novel data-driven criterion called Information Criterion via Data Thinning (ICDT), leveraging the thinning property of the Poisson distribution. Unlike traditional data splitting, data thinning partitions the count matrix into training and validation sets while preserving both the distribution and the underlying data structure. Interestingly, the validation error can be decomposed into the training error plus a covariance penalty. A simple estimator of the covariance penalty is obtained, leading to the development of ICDT. The selection consistency of ICDT is derived when both the sample size and the number of variables diverge to infinity. The proposed methodology is extended to dimension reduction in regression by incorporating the response inversely into the Poisson factor model. Extensive simulated examples and two real data applications are used to evaluate the performance of ICDT and compare it with existing criteria. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.