Imputing single cell RNA sequencing data: Mathematical, statistical and computational challenges

估算单细胞 RNA 测序数据：数学、统计和计算挑战

• 批准号: 9902859
• 负责人: Eric C Chi
• 金额: $ 25万
• 依托单位: NORTH CAROLINA STATE UNIVERSITY RALEIGH
• 依托单位国家: 美国
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-09-23 至 2022-08-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/9902859
• 关键词: Address; Algorithms; Biological; Biological Process; Biology; Cells; Complex; Data; Detection; Development; Disease; Dropout; Genes; Genetic Transcription; Genomics; Goals; Healthcare; Individual; Instruction; Joints; Lead; Learning; Malignant Neoplasms; Mathematics; Measurement; Measures; Methods; Modeling; Output; Patients; Play; RNA; Recovery; Research Personnel; Role; Technology; base; cell type; clinical implementation; computerized tools; high dimensionality; insight; mathematical theory; novel; novel strategies; personalized medicine; reconstruction; single-cell RNA sequencing; statistics; theories; tool

Novel single cell RNA sequencing (scRNA-seq) technologies can simultaneously measure the expression levels of all 30,000 genes over thousands to millions of individual cells. The analysis of scRNA-seq data has already led to fundamental advances in biology, including discovery of new cell types, detection of subtle differences between similar cells, and reconstruction of cellular developmental trajectories. Single- cell measurements involve amplification of tiny amounts of RNA and result in extremely sparse data matrices with many zeros, While some of these zeros are due to missing data (dropouts), others represent true biological inactivity. Yet, many scRNA-seq imputation methods treat all observed zero entries identically, leading to imputed matrices that often overestimate transcriptional activity. Other methods that do attempt to distinguish biological zeros from dropouts lack rigorous theoretical guarantees. The goals of this proposal are to develop models, supporting mathematical theory, and computational tools that explicitly take the existence of true biological zeros into account. Matrix imputation under this constraint involves both computational challenges as well as theoretical questions in random matrix theory and high dimensional statistics. These include rank estimation and low rank sparse matrix recovery from partially observed data, and biclustering in the presence of dropouts and zeros, We plan to develop novel approaches based on non-smooth continuous optimization, and derive accompanying statistical guarantees, We also plan to develop ensemble learning approaches that cleverly combine the outputs of multiple imputation algorithms. Finally, we hope to gain important insights regarding recovery from such data via a study of minimax rates and information lower bounds. To address these challenges, we will build on our promising preliminary results and the joint expertise of the investigators in spectral methods, high dimensional statistics, matrix analysis, numerical optimization, and genomics.

新型的单细胞RNA测序（SCRNA-SEQ）技术可以同时测量所有的表达水平 30,000个基因超过数千至数百万个单个细胞。 SCRNA-seq数据的分析已经导致 生物学的基本进步，包括发现新细胞类型，发现之间的细微差异 类似的细胞，以及细胞发育轨迹的重建。单细胞测量涉及 放大少量的RNA，并在许多零中导致非常稀疏的数据矩阵，而其中一些则导致数据矩阵 这些零是由于缺少数据（辍学）所致，其他零代表了真正的生物学不活动。但是，许多scrna-seq 插补方法对所有观察到的零条目的处理相同，导致估算的矩阵通常高估 转录活动。其他尝试区分生物零与辍学的方法缺乏严格的 理论保证。该建议的目标是开发模型，支持数学理论以及 明确考虑了真正的生物零的存在的计算工具。矩阵插补 该约束涉及随机矩阵理论中的计算挑战以及理论问题 高维统计。这些包括排名估计和低等级稀疏矩阵从部分中恢复 观察到的数据以及在辍学和零的存在下进行的，我们计划基于 非平滑持续优化，并获得随附的统计保证，我们还计划开发 合奏学习方法巧妙地结合了多种归档算法的输出。最后，我们希望 通过研究最小值和信息较低 边界。为了应对这些挑战，我们将以我们有希望的初步结果和共同专业知识为基础 光谱方法的研究者，高维统计，基质分析，数值优化和基因组学。