AI 中文总结
针对广义双线性模型在样本协变量增多时效率下降的问题，提出降秩广义双线性模型，通过降秩样本系数矩阵提升性能，开发数据精简方法用于模型选择，并将其应用于胰腺癌Perturb-seq数据。
AI 中文摘要
降维与效应估计是基因组学等高维数据分析的核心任务。广义双线性模型（Generalized Bilinear Models, GBMs）是完成这些任务的通用框架，但当样本协变量数量增加时，GBMs的统计效率与计算效率会迅速下降。为解决这一局限，我们提出降秩广义双线性模型（reduced-rank generalized bilinear models, RR-GBMs），该模型采用降秩样本系数矩阵对大量协变量的效应进行建模，无需过多参数。模拟研究显示，当真实样本系数矩阵为降秩或接近降秩时，RR-GBM在统计性能与计算效率上均优于标准满秩GBM，能以更低计算负担提供更准确的估计。我们开发了RR-GBM框架中用于模型选择的数据精简方法，便于秩选择。此外，RR-GBM还提供了一种新的协变量与特征间关系的可视化方法，我们将该方法应用于胰腺癌的Perturb-seq数据进行验证。
英文摘要
Dimensionality reduction and effect estimation are central tasks in the analysis of high-dimensional data such as in genomics. Generalized bilinear models (GBMs) provide a versatile framework for these tasks, however, the statistical and computational efficiency of GBMs degrades rapidly as the number of sample covariates grows. To address this limitation, we introduce reduced-rank generalized bilinear models (RR-GBMs), which employ a reduced-rank sample coefficient matrix to model the effect of a large number of covariates without requiring an excessive number of parameters. In simulation studies, we find that when the true sample coefficient matrix is reduced rank or close to reduced rank, RR-GBM outperforms the standard full-rank GBM both statistically and computationally, providing more accurate estimates with lower computational burden. We develop a data thinning approach for model selection in the RR-GBM framework, facilitating rank selection. Furthermore, RR-GBM enables a new approach to visualizing the relationships among covariates and among features. We demonstrate the method in an application to Perturb-seq data for pancreatic cancer.
