Multi-cellular programs (MCPs) are coordinated patterns of gene expression across interacting cell types that collectively drive complex biological processes such as tissue development and immune responses. While MCPs are typically estimated from high-dimensional gene expression data using methods like sparse principal component analysis or latent factor models, these approaches often suffer from high computational costs and limited statistical power. In this work, we propose Sparse Group Principal Component Analysis (SGPCA) to estimate MCPs by leveraging their inherent group and individual sparsity. We introduce an efficient double-thresholding algorithm based on power iteration. In each iteration, a group thresholding step first identifies relevant gene groups, followed by an individual thresholding step to select active cell types. This algorithm achieves a linear computational complexity of $O(np)$, making it highly efficient and scalable for large-scale genomic analyses. We establish theoretical guarantees for SGPCA, including statistical consistency and a convergence rate that surpasses competing methods. Through extensive simulations, we demonstrate that SGPCA achieves superior estimation accuracy and improved statistical power for signal detection. Furthermore, We apply SGPCA to a Lupus study, discovering differentially expressed MCPs distinguishing Lupus patients from normal subjects.
Sparse PCA: Phase Transitions in the Critical Regime
Stern School of Business, New York University（纽约大学斯特恩商学院）；Department of Statistics and Data Science, Yale University（耶鲁大学统计与数据科学系）；Department of Mathematics, Texas A&M University（德克萨斯农工大学数学系）
Distinguishing between Normal and Cancer Cells Using Autoencoder Node Saliency
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
基因表达谱已被广泛用于表征细胞对疾病的反应模式。随着数据变得可用，可扩展的学习工具包对于使用深度学习模型来处理大型数据集以模拟复杂的生物过程变得至关重要。我们提出了一个自动编码器来捕获从基因表达谱中恢复的非线性关系。自动编码器是一种使用人工神经网络的非线性降维技术，它学习未标记数据的隐藏表示。我们训练的自动编码器上收集的肿瘤样本从国家癌症研究所基因组数据共享，并获得一个广义和无监督的潜在表示。我们利用专注于HPC的深度学习工具包Livermore Big Artificial神经网络（LBANN）来高效地并行化训练算法，将计算时间从几个小时减少到几分钟。使用经过训练的自动编码器，我们生成了一个小数据集的潜在表示，其中包含各种肿瘤类型的正常细胞和癌细胞对。一种新的措施，称为自动编码器节点显着性（ANS）的介绍，以确定隐藏的节点，最好区分各种对细胞。我们比较我们的最佳分类节点的主成分分析和可视化的t分布随机邻居嵌入的结果。我们证明了自动编码器可以有效地为数据集中的多个学习任务提取不同的基因特征。
