CIF: Small: Nonlinear Matrix and Tensor Completion with Applications in Systems Biology

CIF：小：非线性矩阵和张量补全及其在系统生物学中的应用

• 批准号: 1117980
• 负责人: Olgica Milenkovic
• 金额: $ 47.8万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1117980&HistoricalAwards=false
• 关键词: CIF; Small; Nonlinear; Matrix; Tensor

Many experiments in molecular biology designed for discovering cellular functions and organization, or estimating the efficiency of drug treatments, are prohibitively expensive to be systematically conducted on large scale systems. It is therefore of paramount importance to develop analytical methods for predicting which experiments are likely to provide the most informative outcomes of biological tests, based only on a small sample of incomplete and noisy measurements. Frequently, the incomplete data are random or pseudo-random samples of a matrix, or more generally, a multidimensional array (tensor). This suggests the use of a new algorithmic and analytic paradigm, termed low-rank matrix and tensor completion, for solving the inference problems at hand. This research involves the development of novel tensor and nonlinear completion methods for inference of protein-protein interaction networks and design of synthetic lethality experiments. The methods used represent a combination of information-theoretic and algorithmic approaches centered around constrained optimization on Grassman manifolds. This research program has the potential to benefit many branches of molecular biology, neuroscience, computer vision, control, economics and signal processing in terms of answering fundamental inference questions for sparse systems and reducing the cost and time associated with system testing and experimental design. It will also provide unprecedented opportunities to graduate students in the electrical engineering and mathematics departments at UIUC to explore state-of-the art technologies and research problems at the intersection of molecular biology, bio-informatics, and signal processing.

在分子生物学中，许多旨在发现细胞功能和组织，或估计药物治疗效率的实验，都是非常昂贵的，无法在大规模系统上系统地进行。因此，极为重要的是发展分析方法，仅根据一小部分不完整和有噪声的测量样本，预测哪些实验可能提供最有信息量的生物试验结果。通常，不完整数据是矩阵的随机或伪随机样本，或者更一般地说，是多维数组（张量）。这表明使用一种新的算法和分析范式，称为低秩矩阵和张量补全，来解决手头的推理问题。本研究涉及开发新的张量和非线性补全方法来推断蛋白质-蛋白质相互作用网络和设计合成致死性实验。所使用的方法代表了围绕格拉斯曼流形约束优化的信息论和算法方法的结合。这个研究项目在回答稀疏系统的基本推理问题和减少与系统测试和实验设计相关的成本和时间方面，有可能使分子生物学、神经科学、计算机视觉、控制、经济学和信号处理的许多分支受益。它还将为UIUC电子工程和数学系的研究生提供前所未有的机会，探索分子生物学、生物信息学和信号处理交叉领域的最新技术和研究问题。