CAREER: High Dimensional Statistics -- Adaptive Networks, Structure and Robustness

数据驱动的适应已经成为工程，社会和生物大规模复杂系统中算法设计的一个强大范例。复杂动态网络中的许多现象都是高维的：模型？的维数可以等于或超过可以收集的数据点或可以执行的实验的数量。这种新的制度提出了严峻的算法，计算和分析的挑战。智力优点：低维结构？在许多复杂的系统中经常隐藏但普遍存在？提供了前进的方向。我们提出了一个基本上完整的重新思考鲁棒优化：想象虚构的参数不确定性，我们设计了一个新的算法框架，发现和利用结构。这极大地拓宽了问题的范围，其中结构可以利用，统一的结果，以前似乎脱节，并打开大门，设计新的高效和可证明有效的算法。然后，从高维统计的工具，强大的优化与结婚的基本思想，我们探讨潜在的严重数据损坏的高维鲁棒性？更广泛的影响：课程倡议包括在新课程中纵向和横向整合数据驱动技术。这项工作将影响并受到与行业合作伙伴的强大联系的激励。高维数据将变得越来越普遍（测序的基因组长度增加;携带遗传疾病的患者数量不会增加）。许多对社会、科学和我们的未来至关重要的问题从根本上依赖于对高维区域的成功分析和高效、鲁棒的算法;对真实的应用的影响将是巨大的。

Data-driven adaptation has emerged as a powerful paradigm for algorithm design in engineered, social, and biological large-scale complex systems. Many phenomena in complex dynamical networks are naturally high dimensional: a model?s dimensionality may equal or exceed the number of data points one can collect or experiments one can perform. This novel regime poses severe algorithmic, computational and analytical challenges.Intellectual Merit: Low-dimensional structure ? often hidden but prevalent in many complex systems ? offers a way forward. We propose an essentially complete rethinking of Robust Optimization: imagining fictitious parameter uncertainty we design a new algorithmic framework for finding and exploiting structure. This greatly broadens the scope of problems where structure can be exploited, unifying results that previously seemed disconnected, and opening the door for the design of new efficient and provably effectivealgorithms. Then, marrying essential ideas of robust optimization with tools from high-dimensional statistics, we explore robustness to potentially severe data corruption in high-dimensions ? a problem that classical robust statistics has largely been unable to address.Broader Impacts: Curriculum initiatives include a vertical and horizontal integration of data-driven techniques in new curriculum. The work will influence and be motivated by strong connections to industry partners. High-dimensional data will become increasingly pervasive (the length of genomes sequenced increases; the number of patients carrying a genetic disease does not). Many questions critical to society, science and our future depend fundamentally on successful analysis and efficient, robust algorithms for the high dimensional regime; the impact to real applications promises to be immense.