Computation of Large-Scale, Multi-Dimensional Sparse Optimization Problems

大规模、多维稀疏优化问题的计算

基本信息

  • 批准号:
    1317602
  • 负责人:
  • 金额:
    $ 30万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2013
  • 资助国家:
    美国
  • 起止时间:
    2013-09-01 至 2016-08-31
  • 项目状态:
    已结题

项目摘要

The proposed research largely lies in sparse optimization, a new distinct area of research in optimization for discovering sparse or other simple-structured solutions from dense datasets. Its development draws algorithmic techniques from classical nonlinear programming and is nurtured by the development in many other areas of data science. Today, the size, complexity, and diversity of instances have grown significantly. The proposed research addresses these new challenges in the following directions: data and variable splitting for handling multiple regularizers and for parallel and distributed optimization, efficient model path computation and regularization parameter selection, stochastic approximation, and coordinate descent methods for non-convex optimization. These investigations are expected to significantly reduce the running times of the existing algorithms, giving rise to novel algorithms to enable the solutions of a wide ranges of problems that are currently not solvable in data sciences. In particular, the expected results will fit machine learning models to data previously inaccessible (e.g., distributed data), enable the mining of data in much higher dimensions and across different modalities, as well as handle multiple regularizers in a computationally tractable way.Technological advances in data gathering have led to a rapid proliferation of big data in diverse areas such as the Internet, engineering, climate studies, cosmology, and medicine. In order for this massive amount of data to make sense, new computational approaches are being introduced to let scientists and engineers analyze their data. Among these approaches, sparse optimization and structured solutions have grown enormously important. Today, their scopes are quickly expanding. Beyond the sensing and processing of 1D signals and 2D images, high-dimensional quantities such as 3D video, 4D CT, and multi-way tensors have become the data or unknown variables in models. Beyond the sparsity structure, structures such as low-rankness, sparse graph, tree structure, linear representation of a few dictionary atoms, as well as their combinations, have debut as desired structures in various applications including genome mapping, protein structure study, social network analysis, stock price prediction, and text/speech mining. The proposed research will build on the recent successes and lead to new techniques for handling large-sized, diverse-typed data and variables, novel algorithms for pursuing a variety of structures in solutions, the extension of existing numerical methods to parallel and decentralized computing architectures, and the contributions to solving key problems in several aforementioned application areas.
拟议的研究主要在于稀疏优化,这是优化领域的一个新的独特研究领域,用于从密集数据集中发现稀疏或其他简单结构的解决方案。它的发展从经典的非线性规划中汲取了算法技术,并受到数据科学许多其他领域的发展的滋养。如今,实例的规模、复杂性和多样性都显著增长。所提出的研究解决了这些新的挑战,在以下方向:数据和变量分裂处理多个正则化和并行和分布式优化,有效的模型路径计算和正则化参数选择,随机逼近,非凸优化和坐标下降方法。这些研究预计将显着减少现有算法的运行时间,从而产生新的算法,以解决目前在数据科学中无法解决的各种问题。特别是,预期的结果将使机器学习模型适合先前不可访问的数据(例如,分布式数据),能够在更高的维度和不同的模式下挖掘数据,并以计算上易于处理的方式处理多个正则化器。数据收集方面的技术进步导致大数据在互联网、工程、气候研究、宇宙学和医学等不同领域迅速扩散。为了让这些海量数据变得有意义,人们正在引入新的计算方法,让科学家和工程师分析他们的数据。在这些方法中,稀疏优化和结构化解决方案变得非常重要。今天,他们的范围正在迅速扩大。除了1D信号和2D图像的传感和处理之外,3D视频、4D CT和多路张量等高维量已成为模型中的数据或未知变量。除了稀疏性结构之外,诸如低秩、稀疏图、树结构、一些字典原子的线性表示以及它们的组合之类的结构已经在各种应用中作为期望的结构首次亮相,包括基因组作图、蛋白质结构研究、社会网络分析、股票价格预测和文本/语音挖掘。拟议的研究将建立在最近的成功,并导致新的技术来处理大规模的,不同类型的数据和变量,新的算法,追求各种结构的解决方案,现有的数值方法的扩展并行和分散的计算架构,并有助于解决上述几个应用领域的关键问题。

项目成果

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Wotao Yin其他文献

ExtraPush for consensus optimization with convex differentiable objective functions over a directed network
ExtraPush 通过有向网络上的凸可微目标函数实现共识优化
Learning Collaborative Sparsity Structure via Nonconvex Optimization for Feature Recognition
通过非凸优化学习协作稀疏结构进行特征识别
One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations
l1 综合和 l1 分析最小化的解决方案唯一性和鲁棒性的一个条件
Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs
(混合整数)二次规划的图神经网络的表达能力
  • DOI:
  • 发表时间:
    2024
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Ziang Chen;Xiaohan Chen;Jialin Liu;Xinshang Wang;Wotao Yin
  • 通讯作者:
    Wotao Yin
Decentralized jointly sparse signal recovery by reweighted lq minimization
通过重新加权 lq 最小化分散式联合稀疏信号恢复

Wotao Yin的其他文献

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{{ truncateString('Wotao Yin', 18)}}的其他基金

Operator Splitting Methods: Certificates and Second-Order Acceleration
算子拆分方法:证书和二阶加速
  • 批准号:
    1720237
  • 财政年份:
    2017
  • 资助金额:
    $ 30万
  • 项目类别:
    Standard Grant
EAGER- DynamicData: Novel Approaches for Optimization, Control, and Learning in Distributed Networks
EAGER-DynamicData:分布式网络中优化、控制和学习的新方法
  • 批准号:
    1462397
  • 财政年份:
    2015
  • 资助金额:
    $ 30万
  • 项目类别:
    Standard Grant
CAREER: Optimizations for Sparse Solutions and Applications
职业:稀疏解决方案和应用程序的优化
  • 批准号:
    1349855
  • 财政年份:
    2013
  • 资助金额:
    $ 30万
  • 项目类别:
    Continuing Grant
CAREER: Optimizations for Sparse Solutions and Applications
职业:稀疏解决方案和应用程序的优化
  • 批准号:
    0748839
  • 财政年份:
    2008
  • 资助金额:
    $ 30万
  • 项目类别:
    Continuing Grant

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