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AitF: Collaborative Research: Efficient High-Dimensional Integration using Error-Correcting Codes

AitF：协作研究：使用纠错码进行高效高维积分

基本信息

批准号：
1733884
负责人：
Jose Garcia-Luna-Aceves
金额：
$ 43.82万
依托单位：
University of California-Santa Cruz
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2021-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1733884&HistoricalAwards=false
关键词：
AitF Collaborative Research Efficient Dimensional

项目摘要

Efficiently estimating integrals of high-dimensional functions is a fundamental and largely unsolved computational problem, manifesting in scientific areas from biology and physics to economics. In particular, in Artificial Intelligence and Machine Learning, a wide array of methods are computationally limited precisely because they require the computation of high-dimensional integrals. While computing such integrals exactly is highly intractable, approximations suffice for many applications. Currently, approximation is attempted using two main classes of algorithms: Markov Chain Monte Carlo (MCMC) sampling methods and variational inference techniques. The former are asymptotically accurate, but their computational budget is inflexible and often prohibitive. The latter have manageable computational budget, but typically come with no accuracy guarantees. This project will investigate a new family of computationally efficient approximation methods which reduce the task of integration to the much better studied task of optimization, thus leveraging decades of research and engineering in combinatorial optimization methods and technology. A key goal of the project is to develop an open-source software library of efficient tools for high-dimensional integration.The reduction of integration to optimization builds on the probabilistic reduction of decision problems to uniqueness promise problems developed in the mid-80s. Specifically, the idea is to use systems of random parity equations in order to specify random subsets of the function's domain, and relate integration to the task of optimization over these subsets. In general, the capacity for efficient optimization fundamentally stems from the capacity to summarily dispense large parts of the domain as uninteresting. The key question to be addressed by the project is whether it is possible to define random subsets over which optimization is both tractable and informative for integration. To that end, the project will employ random systems of linear equations corresponding to Low Density Parity Check (LDPC) matrices for error-correcting codes. The energy landscape, i.e., the number of violated equations, of such systems is far smoother than that of the generic (dense) random systems of linear equations that underlie the original mid-80s technique, thus being far more amenable to optimization. The project will also build upon the deep understanding gained in the last two decades for LDPC codes in the field of communications, with the goal of integrating a priori knowledge about the energy landscape in the optimization strategy. This will provide a fundamentally new use for error-correcting codes, creating a bridge between the areas of optimization and information theory.

有效地估计高维函数的积分是一个基本的和在很大程度上没有解决的计算问题，体现在从生物、物理到经济的科学领域。特别是，在人工智能和机器学习中，大量的方法在计算上受到限制，因为它们需要计算高维积分。虽然精确地计算这样的积分是非常困难的，但近似对于许多应用来说已经足够了。目前，主要使用两类算法进行逼近：马尔可夫链蒙特卡罗(MCMC)抽样方法和变分推理技术。前者是渐近准确的，但它们的计算预算不灵活，而且往往令人望而却步。后者有可管理的计算预算，但通常没有精度保证。这个项目将研究一系列新的计算高效的近似方法，将积分任务减少到研究得更好的优化任务，从而利用几十年来在组合优化方法和技术方面的研究和工程。该项目的一个关键目标是开发一个开放源码软件库，其中包含用于高维集成的有效工具。从集成到优化的简化建立在80年代中期开发的决策问题到唯一性承诺问题的概率简化的基础上。具体地说，这个想法是使用随机奇偶方程系统来指定函数域的随机子集，并将积分与这些子集上的优化任务联系起来。一般而言，有效优化的能力从根本上源于将领域的大部分简单地分配为不感兴趣的能力。该项目要解决的关键问题是，是否有可能定义随机子集，在这些子集上，优化既容易处理，又能为集成提供信息。为此，该项目将采用与低密度奇偶校验(LDPC)矩阵相对应的线性方程随机系统进行纠错编码。这种系统的能量格局，即违反方程的数量，比作为原始80年代中期技术基础的通用(密集)线性方程系统的能量格局要平滑得多，因此更容易进行优化。该项目还将建立在过去二十年在通信领域对LDPC码的深入了解的基础上，目标是将关于能源格局的先验知识整合到优化战略中。这将为纠错码提供一个全新的用途，在优化领域和信息论之间建立一座桥梁。

项目成果

期刊论文数量（6）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Named-Data Transport: An End-to-End Approach for an Information-Centric IP Internet

DOI：
10.1145/3405656.3418714
发表时间：
2020-09
期刊：
Proceedings of the 7th ACM Conference on Information-Centric Networking
影响因子：
0
作者：
A. Albalawi;J. Garcia-Luna-Aceves
通讯作者：
A. Albalawi;J. Garcia-Luna-Aceves

Connection-Free Reliable and Efficient Transport Services in the IP Internet

DOI：
10.23919/cnsm50824.2020.9269115
发表时间：
2020-11
期刊：
2020 16th International Conference on Network and Service Management (CNSM)
影响因子：
0
作者：
J. Garcia-Luna-Aceves;A. Albalawi
通讯作者：
J. Garcia-Luna-Aceves;A. Albalawi

Queue-Sharing Multiple Access

队列共享多路访问

DOI：
10.1145/3416010.3423230
发表时间：
2020
期刊：
MSWiM '20
影响因子：
0
作者：
Garcia-Luna-Aceves, J.J.;Cirimelli-Low, Dylan
通讯作者：
Cirimelli-Low, Dylan

Fast Sampling of Perfectly Uniform Satisfying Assignments

DOI：
10.1007/978-3-319-94144-8_9
发表时间：
2018-07
期刊：
影响因子：
0
作者：
D. Achlioptas;Zayd Hammoudeh;P. Theodoropoulos
通讯作者：
D. Achlioptas;Zayd Hammoudeh;P. Theodoropoulos

A Connection-Free Reliable Transport Protocol

DOI：
10.1109/ipccc50635.2020.9391540
发表时间：
2020-11
期刊：
2020 IEEE 39th International Performance Computing and Communications Conference (IPCCC)
影响因子：
0
作者：
J. Garcia-Luna-Aceves;A. Albalawi
通讯作者：
J. Garcia-Luna-Aceves;A. Albalawi