2015 Gene Golub SIAM Summer School (G2S3): Randomization in Numerical Linear Algebra (RandNLA)

该项目支持约25名在Gene Golub SIAM暑期学校的美国博士生的参与。暑期学校将于2015年6月15日至26日在希腊德尔菲的欧洲文化中心举行，主题是“数值线性代数中的随机化（RandNLA）”。随机化，当它归结为它时，等于玩骰子和冒险。乍一看，这似乎是一种不合情理的科学调查方法。然而，随机化可以追溯到1946年的洛斯阿拉莫斯国家实验室，在那里，约翰·冯·诺伊曼、斯坦尼斯拉夫·乌拉姆和尼古拉斯·大都会设计了蒙特卡罗方法来模拟中子的行为，以达到屏蔽辐射的目的。如果应用得当，并且在统计上非常谨慎，随机抽样可以将数据洪流减少到可管理的数量。具体来说，RandNLA是一个新的跨学科领域，其目标是在数据挖掘、信息检索和互联网建模方面的大数据应用，以及更传统的领域，如遗传学和天文学。难点在于在面对随机化时保证可靠性和可预测的行为。RandNLA方法的开发和分析需要应用数学、统计学、计算机科学和优化方面的创新工具。暑期学校将为学生们提供一个跨学科的教育，这个领域太新鲜了，以至于没有教科书。他们将学习线性代数、概率论、数值方法、算法理论和凸优化的相关理论基础；他们将接触到数据分析和机器学习方面的应用。学生还将互动参与结合算法设计、数值实现和对真实数据的实证评估的项目。关于这个暑期学校的更多信息可以在http://scgroup19.ceid.upatras.gr/g2s32015/上找到。

This project supports the participation of about 25 US based Ph.D. students at the Gene Golub SIAM Summer School. The Summer School will take place 15-26 June 2015, at the European Cultural Centre of Delphi, in Greece, and the topic is "Randomization in Numerical Linear Algebra (RandNLA)". Randomization, when it comes down to it, amounts to playing dice and taking chances. At first sight it appears to be an unconscionable approach for a scientific investigation. However, randomization goes back to Los Alamos National Laboratory in 1946, where John von Neumann, Stanislaw Ulam and Nicholas Metropolis designed Monte Carlo methods to model the behavior of neutrons for the purpose of radiation shielding. When applied judiciously and with great statistical care, randomized sampling can reduce a data deluge to a manageable volume.RandNLA, specifically, is a new interdisciplinary area that targets big data applications in data mining, information retrieval, and internet modeling, as well as more traditional areas like genetics and astronomy. The difficulty is guaranteeing reliability and predictable behaviour in the face of randomization. The development and analysis of RandNLA methods requires innovative tools from applied mathematics, statistics, computer science, and optimization. The summer school will give the students an interdisciplinary education in an area that is too fresh to have produced textbooks. They will learn the relevant theoretical foundations in linear algebra, probability theory, numerical methods, theory of algorithms, and convex optimization; and they will be exposed to applications in data analysis and machine learning. The students will also interactively participate in projects that combine algorithm design, numerical implementations, and empirical evaluations on real data. More information about this summer school can be found at http://scgroup19.ceid.upatras.gr/g2s32015/.