Advanced Models and Algorithms for Large-Scale High-Dimensional Probabilistic Graph Structure Learning

大规模高维概率图结构学习的先进模型和算法

• 批准号: 2009689
• 负责人: Li Wang
• 金额: $ 29.01万
• 依托单位: University of Texas at Arlington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2009689&HistoricalAwards=false
• 关键词: Advanced; Models; Algorithms; Large; Scale

With the rapid development of science and technology, vast amount of data has been and is being collected in nearly all fields of science and engineering for various practical purposes, such as medical data for advancing human knowledge in diseases and treatments to save lives, image data from the solar system and beyond for human's next frontier in space, and social network data for better understanding the society and economic developments. But to make these aims realities, data must be soundly analyzed to uncover what matters. While data analysis has been around for centuries, today's data is much bigger in amount and dimension and more complex, presenting notorious challenges to modern data analysis. Often real world data is noisy and conceals inherent hidden structures that can be concisely represented by graphs that use nodes for objects/events and edges for relations between nodes. Existing approaches rely on pre- and heuristically constructible graphs show their inability in handling nowadays complicated data. This project aims to change the status quo by developing novel mathematical models and efficient computational tools for scientists, engineers, and medical professionals who can use the models and tools to unearth the hidden structures to achieve scientific discoveries previously considered impossible. The principle investigators will integrate their research activities of this project with teaching and education, and will train undergraduate and graduate students in computational mathematics, data science, and interdisciplinary studies.The proposed research will result in advanced models and efficient algorithms for graph-based machine learning. Two major distinctions from existing graph-based learning methods are (1) new models have a built-in probabilistic component that can robustly deal with high noisy data, and (2) a dynamic graph structure learning component that can uncover hidden graph structures concealed in real world data and yet not obvious enough to be pre- or heuristically constructed. The models have much wider applicability than existing graph-based learning methods because graph structure is now a variable that will be optimized over so as to yield an optimal hidden graph structure for a given data set, and the algorithms not only are capable of producing robust embeddings with simultaneously learned hidden graph structures but also will be made practical for big data through landmark and low-rank matrix approximation strategies. The proposed research will have potentially high impacts scientifically in areas where analyzing high-dimensional datasets plays critically important roles, such as data visualization, discovering structural patterns in computational biology, brain networks and other areas. The project will open up a new research direction in statistical machine learning.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.

随着科学和技术的快速发展，出于各种实际目的，已经并且正在在几乎所有的科学和工程领域中收集大量数据，例如用于促进人类知识的医学数据，以促进疾病和治疗方面的人类知识，以挽救生命，从太阳系及其超越人类的下一个领域的图像数据，以及在太空领域的下一个领域以及社交网络数据，以更好地理解社会和经济发展。但是，为了使这些目标现实，必须分析数据以发现重要的事情。尽管数据分析已经存在了几个世纪，但当今的数据的数量和维度更大，更复杂，对现代数据分析提出了臭名昭著的挑战。现实世界中的数据通常是嘈杂的，并且隐藏了固有的隐藏结构，这些结构可以由将节点用于对象/事件的图表和边缘用于节点之间关系的图表。现有的方法依赖于前和启发式构造的图表，表明它们无法处理当今的复杂数据。该项目旨在通过为科学家，工程师和医学专业人员开发新颖的数学模型和有效的计算工具来改变现状，他们可以使用模型和工具来发掘隐藏的结构，以实现先前认为不可能的科学发现。原则研究人员将将其该项目的研究活动与教学和教育相结合，并将培训计算数学，数据科学和跨学科研究的本科生和研究生。拟议的研究将导致基于图形的机器学习的高级模型和有效的算法。现有基于图的学​​习方法的两个主要区别是（1）新模型具有一个内置的概率组件，可以牢固地处理高嘈杂的数据，并且（2）动态的图形结构学习组件，可以揭示隐藏在现实世界中数据中的隐藏图形结构，并且不足以预先或启发性地结构。这些模型的适用性比现有基于图的学​​习方法更广泛，因为图现在已成为一个变量，可以优化，以便为给定的数据集提供最佳的隐藏图结构，并且该算法不仅能够通过同时学习的隐藏图形结构生成可靠的嵌入，而且还可以通过Landmark和低级别的Matrant Matrant Matrant Interrix Intlemations Inticals实用。拟议的研究将在分析高维数据集扮演至关重要的角色的领域中具有很高的影响，例如数据可视化，发现计算生物学，脑网络和其他领域的结构模式。该项目将在统计机器学习方面开辟新的研究方向。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评论标准来评估值得支持的。

项目成果

A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction

• DOI: 10.1007/s10444-022-09929-3
• 发表时间: 2022-03
• 期刊: Advances in Computational Mathematics
• 影响因子: 1.7
• 作者: Xijun Ma;Chungen Shen;Li Wang;Lei-Hong Zhang;Ren-Cang Li

Highly Accurate Latouche-Ramaswami Logarithmic Reduction Algorithm for Quasi-Birth-and-Death Process

准生灭过程的高精度Latouche-Ramaswami对数约简算法

• DOI: 10.4208/jms.v55n2.22.05
• 发表时间: 2022
• 期刊: Journal of Mathematical Study
• 影响因子: 0.8
• 作者: Gu, Guiding;Li, Wang;Li, Ren-Cang
• 通讯作者: Li, Ren-Cang

Sprod for de-noising spatially resolved transcriptomics data based on position and image information.

• DOI: 10.1038/s41592-022-01560-w
• 发表时间: 2022-08
• 期刊: NATURE METHODS
• 影响因子: 48
• 作者: Wang, Yunguan;Song, Bing;Wang, Shidan;Chen, Mingyi;Xie, Yang;Xiao, Guanghua;Wang, Li;Wang, Tao
• 通讯作者: Wang, Tao

On generalizing trace minimization principles

关于推广踪迹最小化原则

• DOI: 10.1016/j.laa.2022.10.012
• 发表时间: 2023
• 期刊: Linear Algebra and its Applications
• 影响因子: 1.1
• 作者: Xin Liang;Li Wang;Lei-Hong Zhang;Ren-Cang Li
• 通讯作者: Ren-Cang Li

Deep Tensor CCA for Multi-View Learning

• DOI: 10.1109/tbdata.2021.3079234
• 发表时间: 2020-05
• 期刊: IEEE Transactions on Big Data
• 影响因子: 7.2
• 作者: Hok Shing Wong;L. xilinx Wang;R. Chan;T. Zeng