Collaborative Research: Bayesian Residual Learning and Random Recursive Partitioning Methods for Gaussian Process Modeling

合作研究：高斯过程建模的贝叶斯残差学习和随机递归划分方法

• 批准号: 2152999
• 负责人: Li Ma
• 金额: $ 12万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-01 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2152999&HistoricalAwards=false
• 关键词: Collaborative; Research; Bayesian; Residual; Learning

Rare natural hazards (for example, storm surge and hurricanes) can cause loss of lives and devastating damage to society and the environment. For instance, Hurricane Katrina (2005) caused over 1,500 deaths and total estimated damages of $75 billion in the New Orleans area and along the Mississippi coast as a result of storm surge. Uncertainty quantification (UQ) has been used widely to understand, monitor, and predict these rare natural hazards. The Gaussian process (GP) modeling framework is one of the most widely used tools to address such UQ applications and has been studied across several areas, including spatial statistics, design and analysis of computer experiments, and machine learning. With the advance of measurement technology and increasing computing power, large numbers of measurements and large-scale numerical simulations at increasing resolutions are routinely collected in modern applications and have given rise to several critical challenges in predicting real-world processes with associated uncertainty. While GP presents a promising route to carrying out UQ tasks for modern emerging applications such as coastal flood hazard studies, existing GP methods are inadequate in addressing several notable issues such as computational bottleneck due to big datasets and spatial heterogeneity due to complex structures in multi-dimensional domains. This project will develop new Bayesian GP methods to allow scalable computation and to capture spatial heterogeneity. The new methods, algorithms, theory, and software are expected to improve GP modeling for addressing data analytical issues across a wide range of fields, including physical science, engineering, medical science, public health, and business science. The project will develop and distribute user-friendly open-source software and provide interdisciplinary research training opportunities for undergraduate and graduate students.This project aims to develop a new Bayesian multi-scale residual learning framework with strong theoretical support that allows scalable computation and spatial nonstationarity for GP modeling. This framework integrates and extends several powerful techniques respectively arising in the literature on GP and that on multi-scale modeling, including predictive process approximation, blockwise shrinkage, and random recursive partitioning on the domain. This framework decomposes the GP into a cascade of residual processes that characterize the underlying covariance structures at different resolutions and that can be spatially heterogeneous in a variety of ways. The new framework allows for adoption of blockwise shrinkage to infer the covariance of the residual processes and incorporates random partition priors to enable adaptivity to various spatial structures in multi-dimensional domains. New recursive algorithms inspired by wavelet shrinkage and state-space models will be developed to achieve linear computational complexity and linear storage complexity in terms of the number of observations. The resulting GP method will guarantee linear computational complexity in a serial computing environment and also be easily parallelizable. This Bayesian multi-scale residual learning method provides a new approach to addressing GP modeling issues among spatial statistics, design and analysis of computer experiments, machine learning, and nonparametric regression.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.

罕见的自然危害（例如，风暴潮和飓风）可能会造成生命丧失，并造成对社会和环境的破坏。例如，卡特里娜飓风（2005年）在新奥尔良地区和密西西比州海岸造成了1,500多人的死亡，估计为750亿美元的赔偿金。不确定性定量（UQ）已被广泛用于理解，监测和预测这些罕见的自然危害。 高斯流程（GP）建模框架是解决此类UQ应用程序的最广泛使用的工具之一，并且已经在多个领域进行了研究，包括空间统计，计算机实验的设计和分析以及机器学习。随着测量技术的进步和提高计算能力，在现代应用中常规收集了大量的测量和大规模的数值模拟，并在预测现实世界中与相关不确定性的现实世界过程中遇到了一些关键挑战。尽管GP提出了针对现代新兴应用（例如沿海洪水危害研究）执行UQ任务的有希望的途径，但现有的GP方法在解决了几个值得注意的问题（例如由于多维域中复杂的结构）而引起的几个值得注意的问题，例如计算瓶颈。该项目将开发新的贝叶斯GP方法，以允许可扩展计算并捕获空间异质性。新方法，算法，理论和软件有望改善GP建模，以解决各种领域的数据分析问题，包括物理科学，工程，医学，医学，公共卫生和商业科学。该项目将开发和分发用户友好的开源软件，并为本科生和研究生提供跨学科的研究培训机会。该项目旨在开发新的贝叶斯多规模剩余学习框架，并具有强大的理论支持，可扩展计算和空间非常规的GP模型。该框架集成并扩展了有关GP的文献和多尺度建模的几种强大技术，包括预测过程近似，区域收缩和域上随机递归分区。该框架将GP分解为一系列剩余过程，这些过程表征了不同分辨率下的基本协方差结构，并且可以通过多种方式在空间上是异质的。新框架允许采用块缩小缩小来推断剩余过程的协方差，并结合随机分区先验，以使对多维域中各种空间结构的适应性适应。将开发受小波收缩和状态空间模型启发的新递归算法，以实现线性计算复杂性和线性存储复杂性，以观测值的数量。所得的GP方法将保证在串行计算环境中线性计算复杂性，并且也很容易平行。这种贝叶斯多尺度剩余学习方法提供了一种新的方法，可以解决针对计算机实验，机器学习和非参数回归的空间统计，设计和分析之间的GP建模问题。该奖项反映了NSF的法定任务，并通过该基金会的智力优点和广泛的影响来评估CRITERIA CRITERIA。