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

数据驱动的自适应已经成为工程、社会和生物大型复杂系统中算法设计的强大范例。复杂动态网络中的许多现象自然是高维的：一个模型？S的维度可能等于或超过一个人可以收集的数据点的数量或一个人可以进行的实验的数量。这种新的制度在算法、计算和分析方面提出了严峻的挑战。智力的优点：低维结构？通常是隐藏的，但在许多复杂系统中很普遍？提供了一条前进的道路。我们提出了一个本质上完整的稳健优化的反思：想象虚拟的参数不确定性，我们设计了一个新的发现和利用结构的算法框架。这极大地扩大了可以利用结构的问题的范围，统一了以前似乎互不关联的结果，并为设计新的高效和被证明有效的算法打开了大门。然后，结合稳健优化的基本思想和来自高维统计的工具，我们探索了对高维潜在严重数据损坏的稳健性？这是一个经典的稳健统计在很大程度上无法解决的问题。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的技术。这项工作将影响和激励与行业合作伙伴的强大联系。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取决于对高维体制的成功分析和高效、健壮的算法；这对实际应用的影响有望是巨大的。

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.