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

许多分子生物学实验旨在发现细胞功能和组织，或估计药物治疗的效率，是昂贵的，无法在大规模系统上系统地进行。因此，至关重要的是，开发分析方法来预测哪些实验可能提供最丰富的生物试验结果，仅基于不完整和噪声测量的小样本。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，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完成，用于解决手头的推理问题。本研究涉及新的张量和非线性完成方法的发展，用于蛋白质-蛋白质相互作用网络的推断和合成致死率实验的设计。所使用的方法代表了信息理论和算法的方法围绕格拉斯曼流形约束优化的组合。该研究计划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，以回答稀疏系统的基本推理问题，并减少与系统测试和实验设计相关的成本和时间。它还将为UIUC电气工程和数学系的研究生提供前所未有的机会，以探索分子生物学，生物信息学和信号处理交叉领域的最先进技术和研究问题。

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.