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

基本信息

批准号：
10021696
负责人：
Eric C Chi
金额：
$ 22.3万
依托单位：
NORTH CAROLINA STATE UNIVERSITY RALEIGH
依托单位国家：
美国
项目类别：
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/10021696
关键词：
Address Algorithms Biological Biological Process Biology Cells Complex Data Detection Development Disease Dropout Genes Genetic Transcription Genomics Goals Healthcare Individual 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

Address Algorithms Biological Biological Process Biology Cells Complex Data Detection Development Disease Dropout Genes Genetic Transcription Genomics Goals Healthcare Individual 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

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项目摘要

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。