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A Global-Local Approximation Framework for Large-Scale Gaussian Process Modeling 大规模高斯过程建模的全局-局部近似框架
IF 2.5 3区 工程技术 Q1 Mathematics Pub Date : 2023-12-18 DOI: 10.1080/00401706.2023.2296451
Akhil Vakayil, V. Roshan Joseph
In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational b...
在这项工作中,我们为大规模高斯过程(GP)建模提出了一个新颖的框架。与文献中为解决计算难题而提出的全局和局部近似方法相反,我们提出了一种用于大规模高斯过程(GP)建模的新框架。
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引用次数: 0
A graphical multi-fidelity Gaussian process model, with application to emulation of heavy-ion collisions 图形化多保真高斯过程模型,应用于重离子碰撞仿真
3区 工程技术 Q1 Mathematics Pub Date : 2023-11-09 DOI: 10.1080/00401706.2023.2281940
Yi Ji, Simon Mak, Derek Soeder, J-F Paquet, Steffen A. Bass
AbstractWith advances in scientific computing and mathematical modeling, complex scientific phenomena such as galaxy formations and rocket propulsion can now be reliably simulated. Such simulations can however be very time-intensive, requiring millions of CPU hours to perform. One solution is multi-fidelity emulation, which uses data of different fidelities to train an efficient predictive model which emulates the expensive simulator. For complex scientific problems and with careful elicitation from scientists, such multi-fidelity data may often be linked by a directed acyclic graph (DAG) representing its scientific model dependencies. We thus propose a new Graphical Multi-fidelity Gaussian Process (GMGP) model, which embeds this DAG structure (capturing scientific dependencies) within a Gaussian process framework. We show that the GMGP has desirable modeling traits via two Markov properties, and admits a scalable algorithm for recursive computation of the posterior mean and variance along at each depth level of the DAG. We also present a novel experimental design methodology over the DAG given an experimental budget, and propose a nonlinear extension of the GMGP via deep Gaussian processes. The advantages of the GMGP are then demonstrated via a suite of numerical experiments and an application to emulation of heavy-ion collisions, which can be used to study the conditions of matter in the Universe shortly after the Big Bang. The proposed model has broader uses in data fusion applications with graphical structure, which we further discuss.Keywords: Computer experimentsGaussian processesgraphical modelsnuclear physicsmulti-fidelity modelingDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.
摘要随着科学计算和数学建模技术的进步,星系形成和火箭推进等复杂的科学现象可以可靠地模拟。然而,这样的模拟可能非常耗时,需要数百万个CPU小时来执行。一种解决方案是多保真度仿真,它使用不同保真度的数据来训练一个有效的预测模型来模拟昂贵的模拟器。对于复杂的科学问题,在科学家的仔细启发下,这种多保真度数据通常可以通过表示其科学模型依赖关系的有向无环图(DAG)联系起来。因此,我们提出了一个新的图形化多保真高斯过程(GMGP)模型,该模型将DAG结构(捕获科学依赖关系)嵌入到高斯过程框架中。我们通过两个马尔可夫性质证明GMGP具有理想的建模特性,并且允许一种可扩展的算法用于沿DAG的每个深度水平递归计算后验均值和方差。我们还在给定实验预算的情况下提出了一种新的DAG实验设计方法,并通过深度高斯过程提出了GMGP的非线性扩展。GMGP的优势随后通过一系列数值实验和模拟重离子碰撞的应用得到了证明,重离子碰撞可用于研究大爆炸后不久宇宙中物质的状况。所提出的模型在具有图形结构的数据融合应用中具有更广泛的用途,我们将进一步讨论这一点。关键词:计算机实验,高斯过程,图形模型,核物理,多保真度建模,免责声明作为对作者和研究人员的服务,我们提供这个版本的已接受稿件(AM)。在最终出版版本记录(VoR)之前,将对该手稿进行编辑、排版和审查。在制作和印前,可能会发现可能影响内容的错误,所有适用于期刊的法律免责声明也与这些版本有关。
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引用次数: 0
A Proportional Intensity Model with Frailty for Missing Recurrent Failure Data 缺失经常性故障数据的具有脆弱性的比例强度模型
3区 工程技术 Q1 Mathematics Pub Date : 2023-11-02 DOI: 10.1080/00401706.2023.2277711
Suk Joo Bae, Byeong Min Mun, Xiaoyan Zhu
AbstractIn some practical circumstances, data are recorded after the systems have begun operations, and data collection is stopped at a predetermined time or after a predetermined number of failures. In such circumstances, incompleteness of various types exists in the aspect of the missing number of failures and their occurrence times beyond the duration of the pilot study. Additionally, multiple repairable systems may present system-to-system variability caused by differences in the operating environments or working loads of individual systems. With respect to left-truncated and right-censored recurrent failure data from multiple repairable systems, we propose a reliability model based on a proportional intensity model with frailty. The frailty model explicitly models unobserved heterogeneity among systems. Covariates incorporated into the proportional intensity model additionally account for the heterogeneity between different operating conditions. To estimate the model parameters for the left-truncated and right-censored recurrent failure data, a Monte Carlo expectation maximization algorithm is proposed. Details of the estimation of the model parameters and the construction of their confidence intervals are examined. A real-world example and simulation studies under various scenarios show prominent applications of the proportional intensity model with frailty to left-truncated and right-censored multiple repairable systems for reliability prediction.1Index Terms: Monte Carlo expectation maximization (MCEM) algorithmnonhomogeneous Poisson processrecurrent failure dataproportional intensity modelrepairable systemDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.
在某些实际情况下,在系统开始运行后记录数据,在预定的时间或预定的故障次数后停止数据收集。在这种情况下,各种类型的不完整性存在于缺失的故障数量和它们的发生时间超过了试点研究的持续时间。此外,多个可修复的系统可能呈现系统到系统的可变性,这是由单个系统的操作环境或工作负载的差异引起的。针对多可修系统的左截右截反复失效数据,提出了一种基于带脆弱性的比例强度模型的可靠性模型。脆弱性模型明确地模拟了系统间未观察到的异质性。纳入比例强度模型的协变量还考虑了不同操作条件之间的异质性。为了估计左截右截反复失效数据的模型参数,提出了一种蒙特卡罗期望最大化算法。详细介绍了模型参数的估计及其置信区间的构造。一个现实世界的例子和各种场景下的仿真研究表明,具有脆弱性的比例强度模型在左截短和右截短的多可修系统可靠性预测中的突出应用。1索引术语:蒙特卡罗期望最大化(MCEM)算法非齐次泊松过程反复失效数据比例强度模型可修复系统免责声明作为对作者和研究人员的服务,我们提供此版本的已接受手稿(AM)。在最终出版版本记录(VoR)之前,将对该手稿进行编辑、排版和审查。在制作和印前,可能会发现可能影响内容的错误,所有适用于期刊的法律免责声明也与这些版本有关。
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引用次数: 0
Towards Improved Heliosphere Sky Map Estimation with Theseus 用Theseus改进日球天空图估计
3区 工程技术 Q1 Mathematics Pub Date : 2023-10-24 DOI: 10.1080/00401706.2023.2271017
Dave Osthus, Brian P. Weaver, Lauren J. Beesley, Kelly R. Moran, Madeline A. Stricklin, Eric J. Zirnstein, Paul H. Janzen, Daniel B. Reisenfeld
AbstractThe Interstellar Boundary Explorer (IBEX) satellite has been in orbit since 2008 and detects energy-resolved energetic neutral atoms (ENAs) originating from the heliosphere. Different regions of the heliosphere generate ENAs at different rates. It is of scientific interest to take the data collected by IBEX and estimate spatial maps of heliospheric ENA rates (referred to as sky maps) at higher resolutions than before. These sky maps will subsequently be used to discern between competing theories of heliosphere properties that are not currently possible. The data IBEX collects present challenges to sky map estimation. The two primary challenges are noisy and irregularly spaced data collection and the IBEX instrumentation’s point spread function. In essence, the data collected by IBEX are both noisy and biased for the underlying sky map of inferential interest. In this paper, we present a two-stage sky map estimation procedure called Theseus. In Stage 1, Theseus estimates a blurred sky map from the noisy and irregularly spaced data using an ensemble approach that leverages projection pursuit regression and generalized additive models. In Stage 2, Theseus deblurs the sky map by deconvolving the PSF with the blurred map using regularization. Unblurred sky map uncertainties are computed via bootstrapping. We compare Theseus to a method closely related to the one operationally used today by the IBEX Science Operation Center (ISOC) on both simulated and real data. Theseus outperforms ISOC in nearly every considered metric on simulated data, indicating that Theseus is an improvement over the current state of the art.DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.
摘要星际边界探测器(IBEX)卫星自2008年以来一直在轨道上运行,探测来自日球层的能量分辨高能中性原子(ENAs)。日球层的不同区域以不同的速率产生ENAs。利用IBEX收集的数据以比以前更高的分辨率估计日球层ENA速率的空间图(称为天空图)具有科学意义。这些天空图随后将被用来辨别目前还不可能的关于日球层性质的相互竞争的理论。IBEX收集的数据对天空地图估计提出了挑战。两个主要的挑战是噪声和不规则间隔的数据收集和IBEX仪器的点扩展函数。从本质上讲,IBEX收集的数据既嘈杂又有偏差,无法用于推断兴趣的底层天象图。在本文中,我们提出了一种称为Theseus的两阶段天空图估计程序。在第一阶段,Theseus利用投影追踪回归和广义加性模型的集成方法,从嘈杂和不规则间隔的数据中估计出模糊的天空图。在第二阶段,忒修斯通过使用正则化将PSF与模糊的地图进行反卷积来模糊天空地图。通过自举计算未模糊的天图不确定度。我们将Theseus与IBEX科学操作中心(ISOC)目前在模拟和实际数据上使用的方法密切相关。在模拟数据上,忒修斯几乎在每一个考虑的指标上都优于ISOC,这表明忒修斯是对当前技术水平的改进。免责声明作为对作者和研究人员的服务,我们提供了这个版本的已接受的手稿(AM)。在最终出版版本记录(VoR)之前,将对该手稿进行编辑、排版和审查。在制作和印前,可能会发现可能影响内容的错误,所有适用于期刊的法律免责声明也与这些版本有关。
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引用次数: 1
Efficient Model-free Subsampling Method for Massive Data 海量数据的高效无模型子抽样方法
3区 工程技术 Q1 Mathematics Pub Date : 2023-10-18 DOI: 10.1080/00401706.2023.2271091
Zheng Zhou, Zebin Yang, Aijun Zhang, Yongdao Zhou
AbstractSubsampling plays a crucial role in tackling problems associated with the storage and statistical learning of massive datasets. However, most existing subsampling methods are model-based, which means their performances can drop significantly when the underlying model is misspecified. Such an issue calls for model-free subsampling methods that are robust under diverse model specifications. Recently, several model-free subsampling methods are developed. However, the computing time of these methods grows explosively with the sample size, making them impractical for handling massive data. In this paper, an efficient model-free subsampling method is proposed, which segments the original data into some regular data blocks and obtains subsamples from each data block by the data-driven subsampling method. Compared with existing model-free subsampling methods, the proposed method has a significant speed advantage and performs more robustly for datasets with complex underlying distributions. As demonstrated in simulation experiments, the proposed method is an order of magnitude faster than other commonly used model-free subsampling methods when the sample size of the original dataset reaches the order of 107. Moreover, simulation experiments and case studies show that the proposed method is more robust than other model-free subsampling methods under diverse model specifications and subsample sizes.Keywords: Big data subsamplingModel robustnessParallel computingUniform designsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.
摘要子抽样在解决海量数据集的存储和统计学习问题中起着至关重要的作用。然而,大多数现有的子采样方法都是基于模型的,这意味着当底层模型被错误指定时,它们的性能会显著下降。这样的问题需要在各种模型规范下具有鲁棒性的无模型子采样方法。近年来发展了几种无模型子抽样方法。然而,这些方法的计算时间随着样本量的增长呈爆炸式增长,使得它们在处理海量数据时不切实际。本文提出了一种有效的无模型子采样方法,该方法将原始数据分割成规则的数据块,通过数据驱动的子采样方法从每个数据块中获取子样本。与现有的无模型子采样方法相比,该方法具有显著的速度优势,并且对于底层分布复杂的数据集具有更强的鲁棒性。仿真实验表明,当原始数据集的样本量达到107数量级时,该方法比其他常用的无模型子采样方法快一个数量级。仿真实验和实例研究表明,在不同的模型规格和子样本量下,该方法比其他无模型子抽样方法具有更强的鲁棒性。关键词:大数据子采样模型鲁棒性并行计算统一设计免责声明作为对作者和研究人员的服务,我们提供此版本的已接受稿件(AM)。在最终出版版本记录(VoR)之前,将对该手稿进行编辑、排版和审查。在制作和印前,可能会发现可能影响内容的错误,所有适用于期刊的法律免责声明也与这些版本有关。
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引用次数: 0
Tensor-based Temporal Control for Partially Observed High-dimensional Streaming Data 基于张量的部分观测高维流数据时间控制
3区 工程技术 Q1 Mathematics Pub Date : 2023-10-16 DOI: 10.1080/00401706.2023.2271060
Zihan Zhang, Shancong Mou, Kamran Paynabar, Jianjun Shi
AbstractIn advanced manufacturing processes, high-dimensional (HD) streaming data (e.g., sequential images or videos) are commonly used to provide online measurements of product quality. Although there exist numerous research studies for monitoring and anomaly detection using HD streaming data, little research is conducted on feedback control based on HD streaming data to improve product quality, especially in the presence of incomplete responses. To address this challenge, this paper proposes a novel tensor-based automatic control method for partially observed HD streaming data, which consists of two stages: offline modeling and online control. In the offline modeling stage, we propose a one-step approach integrating parameter estimation of the system model with missing value imputation for the response data. This approach (i) improves the accuracy of parameter estimation, and (ii) maintains a stable and superior imputation performance in a wider range of the rank or missing ratio for the data to be completed, compared to the existing data completion methods. In the online control stage, for each incoming sample, missing observations are imputed by balancing its low-rank information and the one-step-ahead prediction result based on the control action from the last time step. Then, the optimal control action is computed by minimizing a quadratic loss function on the sum of squared deviations from the target. Furthermore, we conduct two sets of simulations and one case study on semiconductor manufacturing to validate the superiority of the proposed framework.Keywords: Streaming DataHigh DimensionTensorFeedback ControlPartial ObservationDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.
在先进制造过程中,高维(HD)流数据(例如,顺序图像或视频)通常用于提供产品质量的在线测量。尽管利用高清流数据进行监测和异常检测的研究很多,但基于高清流数据的反馈控制以提高产品质量的研究很少,特别是在响应不完全的情况下。针对这一挑战,本文提出了一种新的基于张量的部分观测高清流数据自动控制方法,该方法分为离线建模和在线控制两个阶段。在离线建模阶段,我们提出了一种将系统模型的参数估计与响应数据的缺失值输入相结合的一步法。与现有的数据补全方法相比,该方法(1)提高了参数估计的精度;(2)在更大的待补全数据的秩或缺失率范围内保持了稳定和优越的补全性能。在在线控制阶段,对于每个输入样本,通过平衡其低秩信息和基于上一时间步控制动作的前一步预测结果来输入缺失观测值。然后,通过最小化与目标偏差平方和的二次损失函数来计算最优控制动作。此外,我们还进行了两组仿真和一个半导体制造案例研究,以验证所提出框架的优越性。关键词:流数据高维张量反馈控制部分观测免责声明作为对作者和研究人员的服务,我们提供此版本的已接受稿件(AM)。在最终出版版本记录(VoR)之前,将对该手稿进行编辑、排版和审查。在制作和印前,可能会发现可能影响内容的错误,所有适用于期刊的法律免责声明也与这些版本有关。
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引用次数: 0
Post-Shrinkage Strategies in Statistical and Machine Learning for High Dimensional DataPost-Shrinkage Strategies in Statistical and Machine Learning for High Dimensional Data, Syed Ejaz Ahmed, Feryaal Ahmed, and Bahadir Yüzbaşı, New York: Chapman and Hall/CRC Press, 2023, 408 pp., ISBN 9780367763442 高维数据统计和机器学习中的后收缩策略,Syed Ejaz Ahmed, Feryaal Ahmed, Bahadir y<s:1> zba<e:1>,纽约:Chapman and Hall/CRC出版社,2023,408页,ISBN 9780367763442
3区 工程技术 Q1 Mathematics Pub Date : 2023-10-02 DOI: 10.1080/00401706.2023.2262896
Abdulkadir Hussein
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引用次数: 0
Machine Learning for Knowledge Discovery with R: Methodologies for Modeling, Inference, and PredictionKao-Tai Tsai, Boca Raton, FL: CRC Press, Taylor & Francis Group, LLC, 2022, xiii + 260 pp., $ 88.00, ISBN: 978-1-032-06536-6 (H) 使用R进行知识发现的机器学习:建模,推理和预测的方法蔡高泰,博卡拉顿,佛罗里达州:CRC出版社,泰勒;Francis Group, LLC, 2022, 13 + 260页,$ 88.00,ISBN: 978-1-032-06536-6 (H)
3区 工程技术 Q1 Mathematics Pub Date : 2023-10-02 DOI: 10.1080/00401706.2023.2262891
Aszani Aszani
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引用次数: 0
Computer Age Statistical Inference: Algorithms, Evidence, and Data Science, Student ed.Bradley Efron and Trevor Hastie, UK: Cambridge University Press, 2021, xix + 491 pp., $ 39.99 (pbk), ISBN 978-1-108-82341-8. 《计算机时代统计推断:算法、证据和数据科学》,学生编。布拉德利·埃夫隆和特雷弗·哈斯蒂,英国:剑桥大学出版社,2021年,19 + 491页,39.99美元(每磅),ISBN 978-1-108-82341-8。
3区 工程技术 Q1 Mathematics Pub Date : 2023-10-02 DOI: 10.1080/00401706.2023.2262897
Stan Lipovetsky
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引用次数: 0
A Criminologist’s Guide to R: Crime by the NumbersJacob Kaplan, Boca Raton, FL: Chapman and Hall/CRC Press, Taylor & Francis Group, 2022, 432 pp., ISBN 9781032244075. 犯罪学家的R指南:犯罪的数字雅各布卡普兰,博卡拉顿,佛罗里达州:查普曼和霍尔/CRC出版社,泰勒&;弗朗西斯集团,2022,432页,ISBN 9781032244075。
3区 工程技术 Q1 Mathematics Pub Date : 2023-10-02 DOI: 10.1080/00401706.2023.2262895
Enrique Garcia-Ceja
{"title":"A Criminologist’s Guide to R: Crime by the NumbersJacob Kaplan, Boca Raton, FL: Chapman and Hall/CRC Press, Taylor &amp; Francis Group, 2022, 432 pp., ISBN 9781032244075.","authors":"Enrique Garcia-Ceja","doi":"10.1080/00401706.2023.2262895","DOIUrl":"https://doi.org/10.1080/00401706.2023.2262895","url":null,"abstract":"","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135948236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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Technometrics
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