CIF: Small: Secure and Fast Federated Low-Rank Recovery from Few Column-wise Linear, or Quadratic, Projections

CIF：小型：通过少量列线性或二次投影进行安全快速的联合低秩恢复

基本信息

批准号：
2115200
负责人：
Namrata Vaswani
金额：
$ 56.45万
依托单位：
Iowa State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-07-01 至 2025-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2115200&HistoricalAwards=false
关键词：
CIF Small Secure Fast Federated

项目摘要

Large-scale usage of Internet-of-Things (IoT) devices, smartphones and surveillance cameras has resulted in huge amounts of geographically distributed data in current times. This naturally leads to questions of algorithm design for efficient processing and inference on this data. There is a need to compress (sketch) this data before it can be stored, processed, or transmitted. At the other extreme, in projection-imaging settings, such as magnetic resonance imaging (MRI), computed tomography (CT), Fourier ptychography, or sub-diffraction imaging, data is acquired one sample at a time, making the process very slow. In this scenario as well, data may be distributed, e.g., for a jointly reconstructed functional MR images of different human subjects, with scans that may have been acquired at different hospitals around the country. In many of these settings, privacy concerns dictate that the acquired measurements need to be processed in a federated manner. Moreover, the distributed nature of the data necessitates the design of secure approaches that are robust to attacks by potentially malicious nodes. Both efficient sketching and fast dynamic projection imaging require the ability to recover the true signal or image sequence from highly undersampled measurements. Since the early work on compressed sensing (CS), sparsity and structured sparsity assumptions have been exploited very fruitfully for both type of problems. However, there is limited literature on the use of the low-rank (LR) assumption on signal sequences, and almost none that theoretically analyzes the resulting approaches. This project develops fast, sample-efficient, and federated (private and communication-efficient) algorithms for provably correct subspace learning and low-rank matrix recovery from few column-wise independent linear, or quadratic projections. Extensions to LR plus sparse (LR+S) recovery are also examined. It should be noted that this problem setting is very different from other well-investigated LR recovery problems such as multivariate regression (due to the use of different independent measurement matrices for each signal), LR matrix sensing, or LR matrix completion. The team is investigating the design of Gradient Descent (GD) based solutions that are guaranteed, with high probability, to recover an n x q rank-r matrix from m independent linear projections of each of its q columns with m just large enough to satisfy mq C (n+q) r^2 approximately, and that converge geometrically to the true matrix. Furthermore, this project designs novel secure algorithms that are robust to Byzantine nodes for the above classes of problems. This effort is expected to lead to newer solution approaches and analysis techniques, since commonly used assumptions such as strongly convex cost functions and i.i.d. measurements do not hold in this setting. Finally, this project partially supports the new CyMathKids initiative, whose goal is to provide sustained year-long support and extension in Mathematics to grade-school students from under-funded school districts in Des Moines, Iowa. It is intended to fill some of the academic achievement gaps between disadvantaged students and advantaged ones, and do so while the gaps are still small: the pilot phase focuses on elementary students with a plan to follow the same students through the school years.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

当前时代，大规模使用的设备，智能手机和监视摄像头已导致大量地理分布数据。这自然会导致算法设计问题，以有效地处理和推断该数据。需要在将其存储，处理或传输之前压缩（草图）这些数据。在另一个极端情况下，在投影成像的设置（例如磁共振成像（MRI），计算机断层扫描（CT），傅立叶Ptychography或sub-Diffraction成像中，一次获取一个样品，使得该过程非常慢。在这种情况下，也可以分发数据，例如，对于不同人类受试者的共同重建功能性MR图像，可以在全国各地的不同医院获得扫描。在许多情况下，隐私问题表明，所获得的测量需要以联合方式处理。此外，数据的分布性质需要设计安全的方法，这些方法可以通过潜在的恶意节点进行攻击。有效的素描和快速的动态投影成像都需要从高度不足的测量中恢复真实信号或图像序列的能力。由于早期在压缩感测（CS）上进行的工作，因此针对两种类型的问题都非常有效地利用了稀疏性和结构化的稀疏假设。但是，关于信号序列中低级别（LR）假设的使用的文献有限，而理论上几乎没有分析所得方法。该项目开发快速，样本效率和联合（私人和沟通效率）算法，可证明是正确的子空间学习，并且从少数列独立线性或二次预测中从少数列独立线性或二次预测中恢复了较低的矩阵恢复。还检查了LR加稀疏（LR+S）恢复的扩展。应该注意的是，此问题设置与其他经过良好评价的LR恢复问题（例如多元回归（由于使用每个信号使用不同的独立测量矩阵），LR矩阵传感或LR矩阵完成。该团队正在研究基于梯度下降（GD）解决方案的设计，这些解决方案具有很高的可能性，可以从其每个Q列的M独立线性投影中恢复N X Q级 - R矩阵，其M刚好足以满足MQ C（N+Q）R^2的MQ（N+Q）R^2，并大约收敛到GEOMETRIX。此外，该项目设计了新颖的安全算法，这些算法对上述问题的拜占庭节点具有鲁棒性。预计这项工作将导致更新的解决方案方法和分析技术，因为常用的假设（例如强烈凸成本函数和I.I.D.）在这种情况下，测量不得。最后，该项目部分支持了新的Cymathkids倡议，其目标是向来自爱荷华州得梅因资金不足的学区的年级学生提供长达一年的数学支持和扩展。它旨在填补处于弱势学生和优越的学生之间的一些学术成就差距，并且在差距仍然很小的同时这样做：飞行员阶段着重于基础学生，他们计划在学年中跟随同一学生。这奖反映了NSF的统计任务，反映了通过基金会的智力评估和广泛的评估，并值得通过评估来进行评估。