III: Small: Collaborative Research: Cost-Efficient Sampling and Estimation from Large-Scale Networks

从大规模网络或图中采样和估计结构信息一直是我们理解网络动力学及其丰富应用的核心。马尔可夫链蒙特卡罗（MCMC）已经成为一个更广泛的背景下的图采样，包括估计大图的属性，采样的语料库的文件索引的搜索引擎，采样记录从隐藏的数据库背后的Web表单，确定某些特征的子图和频繁的图形模式匹配的关键使能器。尽管MCMC方法及其定制算法在分析各种形式的图结构数据中的应用广泛，但在以MCMC方法为中心的文献中仍然存在关键的挑战和限制。一个是与采样操作相关联的“成本”消耗/约束，其限制了所获得的总样本的大小，并且对基于所获得的样本的任何估计器的准确性产生负面影响。另一个限制是MCMC的最新进展，特别是建立在有利的不可逆马尔可夫链上的进展，不能用于各种大型图采样任务，因为它们需要底层状态空间的全局知识，缺乏分布实现，不受约束的状态空间，以及简化的成本假设。本研究的目标是充分利用一组爬行采样器的潜力，使采样器的自适应和可能的互动上一个正确构建的图形域，超越目前的现状，在广泛的图形采样任务。具体而言，该项目旨在：（i）建立一个理论框架，通过在给定成本预算的情况下，在有挑战性的访问环境下最佳地平衡样本质量和数量之间的权衡，来构建一套具有成本效益的采样政策，（二）通过充分利用过去的信息，设计一类自适应随机游动，以在所获得的样本上实现最小的时间相关性，并通过控制随机游动，共同实现最大的空间探索，以及（iii）扩展标准MCMC工具包，以更快和更具成本效益地探索可行的子图/配置和图上的计算/优化，沿着广泛的验证，以在现实中创建实用和可用的解决方案。这项研究对广泛的多学科应用具有很高的潜在影响，包括用于统计推断和有效估计的大规模图采样以及用于各学科组合优化的随机算法，该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的学术价值和更广泛的影响审查标准。

Sampling and estimating structural information from large-scale networks or graphs has been central to our understanding of the network dynamics and its rich set of applications. Markov Chain Monte Carlo (MCMC) has been the key enabler for a broader context of graph sampling, including estimating the properties of large graphs, sampling the corpus of documents indexed by search engines, sampling records from hidden databases behind Web forms, identifying subgraphs of certain characteristics and frequent graph pattern matching. Despite versatile applications of the MCMC methods and their customized algorithms for analyzing graph-structured data in various forms, there still exist critical challenges and limitations in the literature centered around the MCMC methods. One is the 'cost' consumption/constraints associated with the sampling operation, which limits the size of total samples obtained and negatively affects the accuracy of any estimator based on the obtained samples. Another limitation is that the recent advances in MCMC, especially built up on favorable non-reversible Markov chains, cannot be leveraged to the various large-graph sampling tasks, due to their required global knowledge of the underlying state space, lack of distribution implementation, unconstrained state space, as well as the simplified cost assumption. The goal of this research is to fully exploit the potentials of a set of crawling samplers by making the samplers adaptive and possibly interactive on a properly constructed graph domain, to transcend the current status-quo in the wide range of graph sampling tasks. Specifically, the project aims to: (i) build a theoretical framework to construct a suite of cost-efficient sampling policies by optimally balancing the tradeoff between the sample quality and quantity under challenged access environments with a given cost budget, (ii) design a class of adaptive random walks by fully exploiting the past information to achieve minimal temporal correlations over the obtained samples and by controlling the random walks collectively to enable maximal space exploration, and (iii) extend the standard MCMC toolkits toward faster and more cost-efficient exploration of feasible subgraphs/configurations and computing/optimization on a graph, along with extensive validations to create practical and usable solutions in reality. This research has a high potential impact on a vast range of multi-disciplinary applications, including sampling large-scale graphs for statistical inference and efficient estimation and randomized algorithms for combinatorial optimizations in various disciplines, where the standard MCMC methods have been dominant but also constrained our understanding.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.