CAREER: Parsimonious Modeling via Matrix Minimization

职业:通过矩阵最小化进行简约建模

基本信息

  • 批准号:
    0847077
  • 负责人:
  • 金额:
    $ 40万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2009
  • 资助国家:
    美国
  • 起止时间:
    2009-09-15 至 2015-08-31
  • 项目状态:
    已结题

项目摘要

Intellectual merit: In many engineering applications, notions of complexity, order or dimension of a model can be expressed by the rank of a matrix, while prior information and model accuracy often correspond to convex constraints on this matrix. Parsimonious Modeling involves the computational problem of minimizing matrix rank subject to convex constraints. Examples include problems in system identification, model reduction, and Euclidean embedding, arising in control, signal processing, and machine learning. The rank minimization problem is known to be computationally intractable in general. The work is inspired by the recently developed framework of compressed sensing for sparse signals. A preliminary work by the PI and her collaborators, points to a rich generalization of this theory from sparse vectors to low-rank matrices, showing that some classes of this hard problem can be solved efficiently. The proposed research builds on advances in compressed sensing and its underlying math, as well as convex optimization. The program has three thrusts: (1) theoretical characterization of classes of rank minimization problems that can be solved efficiently, (2) development of efficient semidefinite programming algorithms for this problem, (3) a focus on applications of rank minimization (e.g., in system identification). This program combines practical impact with conceptual depth, unifying existing notions of parsimony (such as vector sparsity and matrix rank) as well as the computational methods to address them.Broader impact: This program will leverage extensive collaborations between pure mathematicians and engineers, and should motivate research in mathematics in areas not traditionally considered ?applied". Results and computational tools developed can be used by researchers in various application fields. Research from this project will be integrated with the PI's past work into a new project-driven graduate course at UW. Students at all levels will be engaged. A workshop and a mathematical problem solving competition is planned as part of UW's BRIDGE program for incoming women and minority freshman.
智力优点:在许多工程应用中,模型的复杂性、阶数或维数等概念可以用矩阵的秩来表示,而先验信息和模型精度往往对应于该矩阵上的凸约束。简约建模涉及在凸约束下最小化矩阵秩的计算问题。例子包括系统识别,模型简化和欧几里得嵌入,在控制,信号处理和机器学习中出现的问题。已知秩最小化问题一般在计算上是难以处理的。 这项工作的灵感来自于最近开发的稀疏信号压缩感知框架。PI和她的合作者的初步工作,指出了这个理论从稀疏向量到低秩矩阵的丰富推广,表明这个难题的某些类别可以有效地解决。拟议的研究建立在压缩感知及其基础数学以及凸优化的基础上。该方案有三个重点:(1)可以有效解决的秩最小化问题的类别的理论表征,(2)针对该问题的有效半定编程算法的开发,(3)关注秩最小化的应用(例如,系统识别)。该计划结合了概念深度的实际影响,统一了现有的简约概念(如向量稀疏性和矩阵秩)以及解决这些问题的计算方法。更广泛的影响:该计划将利用纯数学家和工程师之间的广泛合作,并应激励传统上不考虑的数学领域的研究?适用”。结果和计算工具的开发,可用于研究人员在各个应用领域。该项目的研究将与PI过去的工作整合到UW的新项目驱动的研究生课程中。各级学生都将参与。作为西澳大学针对新生女性和少数族裔新生的BRIDGE项目的一部分,计划举办一场研讨会和数学问题解决竞赛。

项目成果

期刊论文数量(0)
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Maryam Fazel其他文献

Constrained multiple kernel tracking for human limbs
人体四肢的约束多核跟踪
Image of place as a byproduct of medium: Understanding media and place through case study of Foursquare
  • DOI:
    10.1016/j.ccs.2014.10.002
  • 发表时间:
    2015-03-01
  • 期刊:
  • 影响因子:
  • 作者:
    Maryam Fazel;Lakshmi Priya Rajendran
  • 通讯作者:
    Lakshmi Priya Rajendran
Online Algorithms for Budget-Constrained DR-Submodular Maximization
预算受限 DR 子模最大化的在线算法
  • DOI:
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Omid Sadeghi;Reza Eghbali;Maryam Fazel
  • 通讯作者:
    Maryam Fazel
Investigation of Error Simulation Techniques for Learning Dialog Policies for Conversational Error Recovery
研究用于学习会话错误恢复的对话策略的错误模拟技术
  • DOI:
  • 发表时间:
    2019
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Maryam Fazel;Longshaokan Wang;Aditya Tiwari;Spyros Matsoukas
  • 通讯作者:
    Spyros Matsoukas
EXPRESSO: A Benchmark and Analysis of Discrete Expressive Speech Resynthesis
EXPRESSO:离散表达语音重新合成的基准和分析
  • DOI:
    10.21437/interspeech.2023-1905
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Tu Nguyen;Wei;Antony D'Avirro;Bowen Shi;Itai Gat;Maryam Fazel;Tal Remez;Jade Copet;Gabriel Synnaeve;Michael Hassid;Felix Kreuk;Yossi Adi;Emmanuel Dupoux
  • 通讯作者:
    Emmanuel Dupoux

Maryam Fazel的其他文献

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{{ truncateString('Maryam Fazel', 18)}}的其他基金

TRIPODS: Institute for Foundations of Data Science
TRIPODS:数据科学研究所
  • 批准号:
    2023166
  • 财政年份:
    2020
  • 资助金额:
    $ 40万
  • 项目类别:
    Continuing Grant
TRIPODS+X:EDU: Foundational Training in Neuroscience and Geoscience via Hackweeks
TRIPODS X:EDU:通过 Hackweeks 进行神经科学和地球科学基础培训
  • 批准号:
    1839291
  • 财政年份:
    2018
  • 资助金额:
    $ 40万
  • 项目类别:
    Standard Grant
2015 NSF Early-Career Investigators Workshop on Cyber-Physical Systems for Smart Cities
2015 年 NSF 早期职业研究员智慧城市网络物理系统研讨会
  • 批准号:
    1541730
  • 财政年份:
    2015
  • 资助金额:
    $ 40万
  • 项目类别:
    Standard Grant
CIF: Medium: Collaborative Research: Estimating simultaneously structured models: from phase retrieval to network coding
CIF:媒介:协作研究:估计同时结构化模型:从相位检索到网络编码
  • 批准号:
    1409836
  • 财政年份:
    2014
  • 资助金额:
    $ 40万
  • 项目类别:
    Continuing Grant

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合作研究:CIF:中:通过简约结构了解鲁棒性。
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Collaborative Research: CIF: Medium: Understanding Robustness via Parsimonious Structures.
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Parsimonious high-dimensional and matrix-variate copula modeling
简约高维矩阵变量联结建模
  • 批准号:
    DGECR-2022-00447
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    2022
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    Discovery Launch Supplement
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  • 批准号:
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CAREER: Parsimonious Models for Redistricting
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  • 批准号:
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  • 财政年份:
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CDS
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BIGDATA: IA: Collaborative Research: Parsimonious Anomaly Detection in Sequencing Data
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