CIF: Medium: Collaborative Research: Nonconvex Optimization for High-Dimensional Signal Estimation: Theory and Fast Algorithms
CIF:中:协作研究:高维信号估计的非凸优化:理论和快速算法
基本信息
- 批准号:1806154
- 负责人:
- 金额:$ 40万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2018
- 资助国家:美国
- 起止时间:2018-01-01 至 2021-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
High-dimensional signal estimation plays fundamental roles in various engineering and science applications, such as medical imaging, video and network surveillance. Estimation procedures that maintain both statistical and computational efficacy are of great practical value, which translate into desiderata such as less time patients need to spend in a medical scanner, faster response to cyber attacks, and capabilities to handle very large datasets. While a lot of signal estimation tasks are naturally formulated as nonconvex optimization problems, existing results for nonconvex methods have several fundamental limitations, and the current state of the art is still limited in terms of when, why and which nonconvex approaches are effective for a given problem. The goal of this research program is to significantly deepen and broaden the understanding and applications of nonconvex optimization for high-dimensional signal estimation.In this project, the investigators will study high-dimensional signal estimation via direct optimization of nonconvex, and potentially nonsmooth, loss functions, without resorting to convex relaxation. This research will explore geometric structures shared by nonconvex functions commonly encountered in signal estimation, and study the fundamental roles these structures play in determining the algorithmic convergence. These results will then be exploited as guidelines to develop fast and provably correct algorithms for estimating high-dimensional signals with physically induced structures and under streaming data observations. Specifically, the research program consists of three major thrusts: (1) understanding the geometric structures of important classes of nonconvex loss surfaces, and characterizing their impact on the convergence of optimization algorithms; (2) developing fast algorithms and the associated theory for the recovery of structured low-rank matrices; (3) designing new online algorithms that are time and space efficient under a streaming setting, with the capability of detecting and tracking the time-varying signals of interest.
高维信号估计在医学成像、视频和网络监控等各种工程和科学应用中起着重要的作用。保持统计和计算效率的估计程序具有很大的实用价值,这转化为迫切需要,例如患者需要在医疗扫描仪上花费更少的时间,更快地响应网络攻击,以及处理非常大的数据集的能力。虽然许多信号估计任务自然地被公式化为非凸优化问题,但非凸方法的现有结果具有几个基本限制,并且在何时、为什么以及哪些非凸方法对于给定问题是有效的方面,现有技术仍然是有限的。本研究课题的目的是为了深化和拓宽非凸优化在高维信号估计中的理解和应用。在本课题中,研究人员将通过直接优化非凸的、潜在非光滑的损失函数来研究高维信号估计,而不需要借助凸松弛。本研究将探讨信号估计中常见的非凸函数所共有的几何结构,并研究这些结构在确定算法收敛性方面所起的基本作用。然后,这些结果将被利用作为指导方针,以开发快速和可证明正确的算法,用于估计高维信号与物理诱导的结构和流数据观测。具体而言,该研究计划包括三个主要方向:(1)理解重要类别的非凸损失曲面的几何结构,并表征它们对优化算法收敛性的影响:(2)发展结构低秩矩阵恢复的快速算法和相关理论;(3)设计新的在线算法,其在流设置下是时间和空间有效的,具有检测和跟踪感兴趣的时变信号的能力。
项目成果
期刊论文数量(32)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Tightening the Dependence on Horizon in the Sample Complexity of Q-Learning
- DOI:
- 发表时间:2021-02
- 期刊:
- 影响因子:0
- 作者:Gen Li;Changxiao Cai;Yuxin Chen;Yuantao Gu;Yuting Wei;Yuejie Chi
- 通讯作者:Gen Li;Changxiao Cai;Yuxin Chen;Yuantao Gu;Yuting Wei;Yuejie Chi
Low-Rank Matrix Recovery With Scaled Subgradient Methods: Fast and Robust Convergence Without the Condition Number
使用缩放次梯度方法的低秩矩阵恢复:无需条件数的快速鲁棒收敛
- DOI:10.1109/tsp.2021.3071560
- 发表时间:2021
- 期刊:
- 影响因子:5.4
- 作者:Tong, Tian;Ma, Cong;Chi, Yuejie
- 通讯作者:Chi, Yuejie
Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval and Matrix Completion
非凸统计估计中的隐式正则化:梯度下降线性收敛以进行相位检索和矩阵补全
- DOI:
- 发表时间:2018
- 期刊:
- 影响因子:0
- 作者:Ma, C.;Wang, K.;Chi, Y.;Chen, Y.
- 通讯作者:Chen, Y.
Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
- DOI:10.1109/tsp.2019.2937282
- 发表时间:2019-10-15
- 期刊:
- 影响因子:5.4
- 作者:Chi, Yuejie;Lu, Yue M.;Chen, Yuxin
- 通讯作者:Chen, Yuxin
Streaming PCA and Subspace Tracking: The Missing Data Case
- DOI:10.1109/jproc.2018.2847041
- 发表时间:2018-08-01
- 期刊:
- 影响因子:20.6
- 作者:Balzano, Laura;Chi, Yuejie;Lu, Yue M.
- 通讯作者:Lu, Yue M.
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Yuejie Chi其他文献
Settling the Sample Complexity of Model-Based Offline Reinforcement Learning
解决基于模型的离线强化学习的样本复杂度
- DOI:
10.48550/arxiv.2204.05275 - 发表时间:
2022 - 期刊:
- 影响因子:0
- 作者:
Gen Li;Laixi Shi;Yuxin Chen;Yuejie Chi;Yuting Wei - 通讯作者:
Yuting Wei
Memory-Limited stochastic approximation for poisson subspace tracking
泊松子空间跟踪的内存有限随机近似
- DOI:
- 发表时间:
2017 - 期刊:
- 影响因子:0
- 作者:
Liming Wang;Yuejie Chi - 通讯作者:
Yuejie Chi
Principal subspace estimation for low-rank Toeplitz covariance matrices with binary sensing
具有二元感知的低秩 Toeplitz 协方差矩阵的主子空间估计
- DOI:
10.1109/acssc.2016.7869594 - 发表时间:
2016 - 期刊:
- 影响因子:0
- 作者:
H. Fu;Yuejie Chi - 通讯作者:
Yuejie Chi
Regularized blind detection for MIMO communications
MIMO 通信的正则盲检测
- DOI:
10.1109/isit.2010.5513407 - 发表时间:
2010 - 期刊:
- 影响因子:0
- 作者:
Yuejie Chi;Yiyue Wu;A. Calderbank - 通讯作者:
A. Calderbank
Golay complementary waveforms for sparse delay-Doppler radar imaging
用于稀疏延迟多普勒雷达成像的 Golay 互补波形
- DOI:
- 发表时间:
2009 - 期刊:
- 影响因子:0
- 作者:
Yuejie Chi;Robert Calderbank;A. Pezeshki - 通讯作者:
A. Pezeshki
Yuejie Chi的其他文献
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{{ truncateString('Yuejie Chi', 18)}}的其他基金
Federated Optimization over Bandwidth-Limited Heterogeneous Networks
带宽受限异构网络的联合优化
- 批准号:
2318441 - 财政年份:2023
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
Collaborative Research: Towards a Theoretic Foundation for Optimal Deep Graph Learning
协作研究:为最优深度图学习奠定理论基础
- 批准号:
2134080 - 财政年份:2022
- 资助金额:
$ 40万 - 项目类别:
Continuing Grant
NSF Student Travel Grant for the Fifth Conference on Machine Learning and Systems (MLSys 2022)
第五届机器学习和系统会议 (MLSys 2022) 的 NSF 学生旅费补助金
- 批准号:
2219655 - 财政年份:2022
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
Collaborative Research: CIF: Medium: Statistical and Algorithmic Foundations of Efficient Reinforcement Learning
合作研究:CIF:媒介:高效强化学习的统计和算法基础
- 批准号:
2106778 - 财政年份:2021
- 资助金额:
$ 40万 - 项目类别:
Continuing Grant
Taming Nonlinear Inverse Problems: Theory and Algorithms
驯服非线性反问题:理论与算法
- 批准号:
2126634 - 财政年份:2021
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
CIF: Small: Resource-Efficient Statistical Inference in Networked Environments
CIF:小型:网络环境中资源高效的统计推断
- 批准号:
2007911 - 财政年份:2020
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
CIF: Medium: Collaborative Research: Theory of Optimization Geometry and Algorithms for Neural Networks
CIF:媒介:协作研究:神经网络优化几何理论和算法
- 批准号:
1901199 - 财政年份:2019
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
EAGER-DynamicData: Subspace Learning From Binary Sensing
EAGER-DynamicData:从二进制感知中学习子空间
- 批准号:
1833553 - 财政年份:2018
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
CIF: Small: Inverse Methods for Parametric Mixture Models
CIF:小:参数混合模型的逆方法
- 批准号:
1826519 - 财政年份:2018
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
CAREER: Robust Methods for High-Dimensional Signal Processing under Geometric Constraints
职业:几何约束下高维信号处理的鲁棒方法
- 批准号:
1818571 - 财政年份:2018
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
相似海外基金
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Collaborative Research: CIF: Medium: Fundamental Limits of Cache-aided Multi-user Private Function Retrieval
协作研究:CIF:中:缓存辅助多用户私有函数检索的基本限制
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2312229 - 财政年份:2023
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