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GPU-Accelerated Modified Bessel Function of the Second Kind for Gaussian Processes

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GPU-Accelerated Modified Bessel Function of the Second Kind ...

ISC High Performance 2025 Research Paper Proceedings (40th International Conference)

作者： Zipei Geng Sameh Abdulah Ying Sun Hatem Ltaief David E. Keyes Marc G. Genton Statistics Program King Abdullah University of Science and Technology Thuwal Saudi Arabia Applied Mathematics and Computational Sciences (AMCS) Program King Abdullah University of Science and Technology Thuwal Saudi Arabia

ISBN: (数字)9783982633619

Modified Bessel functions of the second kind are widely used in physics, engineering, spatial statistics, and machine learning. Since contemporary scientific applications, including machine learning, rely on GPUs for acceleration, providing robust GPU-hosted implementations of special functions, such as the modified Bessel function, is crucial for performance. Existing implementations of the modified Bessel function of the second kind rely on CPUs and have limited coverage of the full range of values needed in some applications. In this work, we present a robust implementation of the modified Bessel function of the second kind on GPUs, eliminating the dependence on the CPU host. We cover a range of values commonly used in real applications, providing high accuracy compared to common libraries like the GNU Scientific Library (GSL) when referenced to Mathematica as the authority. Our GPU-accelerated approach also demonstrates a 2.68X performance improvement using a single A100 GPU compared to the GSL on 40-core Intel Cascade Lake CPUs. Our implementation is integrated into ExaGeoStat, the HPC framework for Gaussian process modeling, where the modified Bessel function of the second kind is required by the Matérn covariance function in generating covariance matrices. We accelerate the matrix generation process in ExaGeoStat by up to 12.62X with four A100 GPUs while maintaining almost the same accuracy for modeling and prediction operations using synthetic and real datasets.

关键词： Accuracy Computational modeling Graphics processing units Gaussian processes Machine learning Libraries Computational efficiency Covariance matrices Optimization Synthetic data

Estimation of aboveground biomass of arboreal species in the semi-arid region of Brazil using SAR(synthetic aperture radar)images

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Journal of Arid Land 2023年第6期15卷 695-709页

作者： Janisson B de JESUS Tatiana M KUPLICH Íkaro D de C BARRETO Fernando L HILLEBRAND Cristiano N da ROSA Postgraduate Program in Remote Sensing Federal University of Rio Grande do SulCampus ValePorto Alegre 91501970Brazil National Institute for Space Research(INPE) COESU(Southern Spatial Coordination)Santa Maria 97105970Brazil Postgraduate Program Biometry and Applied Statistics Rural Federal University of PernambucoRecife 52171900Brazil Federal Institute of Education Science and Technology of Rio Grande do Sul(IFRS)Campus RolanteRolante 95690000Brazil Postgraduate Program in Remote Sensing Polar and Climate CenterFederal University of Rio Grande do SulPorto Alegre 91501970Brazil

The Caatinga biome is an important ecosystem in the semi-arid region of *** has significantly degraded due to human activities and is currently a region undergoing ***,monitoring the variation in the Caatinga biome has become essential for its sustainable ***,traditional methods for estimating aboveground biomass(AGB)are time-consuming and *** sensing,such as optical and radar imaging,can estimate and correlate with ***,radar imaging is still a novelty to be applied in estimating the AGB of this biome,which is an area with little ***,this study aimed to use Sentinel-1 images to estimate the AGB of the Caatinga biome in Sergipe State(northeastern Brazil)and to verify its influencing *** sample plots(30 m×30 m)were selected,and the stems of individuals with a circumference at breast height(1.3 m above the ground)equal to or greater than 6.0 cm were measured,and the AGB through an allometric equation was *** Sentinel-1 images from 3 different periods(green,intermediate,and dry periods)were used to consider the phenological conditions of the Caatinga *** the pre-processing and extraction of attributes(co-polarized VV(vertical transmit and vertical receive),cross-polarized VH(vertical transmit and horizontal receive),and band ratio VH/VV backscatter,radar vegetation index,dual polarization synthetic aperture radar(SAR)vegetation index(DPSVI),entropy(H),and alpha angle(α))were performed with Sentinel’s Application *** attributes were used to estimate the AGB through simple and multiple linear regressions and evaluated by the coefficients of determination(R2),correlation(r),and root mean squared error(RMSE).The results showed that the attributes individually had little ability to estimate the AGB of the Caatinga biome in the three *** with multiple regression,we found that the intermediate period presented the equation with the best

关键词： Caatinga tropical dry forest coherent and incoherent attributes C-band Sentinel-1

SUBSPACE METHOD OF MOMENTS FOR AB INITIO 3-D SINGLE-PARTICLE CRYO-EM RECONSTRUCTION

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arXiv 2024年

作者： Hoskins, Jeremy Khoo, Yuehaw Mickelin, Oscar Singer, Amit Wang, Yuguan Departments of Statistics and CCAM University of Chicago Chicago IL 60637 USA Departments of Statistics and CCAM University of Chicago Chicago IL 60637 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA Program in Applied and Computational Mathematics and Department of Mathematics Princeton University Princeton NJ 08544 USA Departments of Statistics University of Chicago Chicago IL 60637 USA

Cryo-electron microscopy (Cryo-EM) is a widely-used technique for recovering the 3-D structure of biological molecules from a large number of experimentally generated noisy 2-D tomographic projection images of the 3-D structure, taken from unknown viewing angles. Through computationally intensive algorithms, these observed images are processed to reconstruct the 3-D structures. Many popular computational methods rely on estimating the unknown angles as part of the reconstruction process, which becomes particularly challenging at low signal-to-noise ratio. The method of moments (MoM) offers an alternative approach that circumvents the estimation of viewing angles of individual projection images by instead estimating the underlying distribution of the viewing angles, and is robust to noise given sufficiently many images. However, the method of moments typically entails computing high-order moments of the projection images, incurring significant storage and computational costs. To mitigate this, we propose a new approach called the subspace method of moments (subspace MoM), which compresses the first three moments using data-driven low-rank tensor techniques as well as expansion into a suitable function basis. The compressed moments can be efficiently computed from the set of projection images using numerical quadrature and can be employed to jointly recover the 3-D structure and the distribution of viewing angles. We illustrate the practical applicability of the subspace MoM in numerical experiments using up to the third-order moment, which significantly improves the resolution of MoM reconstructions compared to previous approaches. Copyright © 2024, The Authors. All rights reserved.

关键词： Image reconstruction

Realistic-science, technology, engineering, and mathematics assisted by google classroom as a learning innovation in the new normal era to improve statistical thinking skill 7

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Realistic-science, technology, engineering, and mathematics ...

7th International Conference on Mathematics, Science, and Education 2020, ICMSE 2020

作者： Ardiansyah, A.S. Novita, N.A. Zhintya, H. Kurnianto, D. Mathematics Education Study Program Universitas Negeri Semarang Indonesia Applied Statistics and Computation Study Program Universitas Negeri Semarang Indonesia

Based on government policies regarding the implementation of learning from home, it is necessary the learning innovation to continue learning in the new normal era by utilizing existing technological advances. In this digital era, statistics thinking is important because it is needed to be able to interpret and understand and make good decisions from the statistical data obtained. From these problems, one of the innovations that can be done is by implementing Realistic Mathematics Education integrated Science, Technology, Engineering, and Mathematics assisted by Google Classroom (R-STEM-GC). This paper aims to determine the effect of R-STEM-GC learning on students' statistical thinking skills. This paper uses literature review method research that identifies, assesses, and interprets all findings on a research topic to answer existing research questions. It can concluded that realistic learning was more effective in terms of students' mathematical reasoning and communication than conventional learning;learning with the application of STEM can improve students' problem solving abilities compared to conventional learning;and the use of google classrooms that can improve communication skills. From the results of this analysis, the application of R-STEM-GC learning can be an innovative solution in improving students' statistical thinking skills in new normal era. © Published under licence by IOP Publishing Ltd.

关键词： Students

EWMA control chart based on its first hitting time and coronavirus alert levels for monitoring symmetric COVID-19 cases

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Asian Pacific Journal of Tropical Medicine 2021年第8期14卷 364-374页

作者： Areepong Yupaporn Sunthornwat Rapin Department of Applied Statistics Faculty of Applied ScienceKing Mongkut's University of Technology North BangkokBangkok 10800Thailand Industrial Technology Program Faculty of Science and TechnologyPathumwan Institute of TechnologyBangkok 10330Thailand

Objective:To define the alert levels for the total number of COVID-19 cases derived by using quantile functions to monitor COVID-19 outbreaks via an exponentially weighted moving-average(EWMA)control chart based on the first hitting time of the total number of COVID-19 cases following a symmetric logistic growth ***:The cumulative distribution function of the time for the total number of COVID-19 cases was used to construct a quantile function for classifying COVID-19 alert *** EWMA control chart control limits for monitoring a COVID-19 outbreak were formulated by applying the delta method and the sample mean and variance *** were selected from countries and region including Thailand,Singapore,Vietnam,and Hong Kong to generate the total number of COVID-19 cases from February 15,2020 to December 16,2020,all of which followed symmetric patterns.A comparison of the two methods was made by applying them to a EWMA control chart based on the first hitting time for monitoring the COVID-19 outbreak in the sampled countries and ***:The optimal first hitting times for the EWMA control chart for monitoring COVID-19 outbreaks in Thailand,Singapore,Vietnam,and Hong Kong were approximately 280,208,286,and 298 days,***:The findings show that the sample mean and variance method can detect the first hitting time better than the delta ***,the COVID-19 alert levels can be defined into four stages for monitoring COVID-19 situation,which help the authorities to enact policies that monitor,control,and protect the population from a COVID-19 outbreak.

关键词： COVID-19 alert levels Symmetric pattern of the total number of COVID-19 cases Monitoring COVID-19 situation EWMA control chart

The Development and Evaluation of Homogenously Weighted Moving Average Control Chart based on an Autoregressive Process

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HighTech and Innovation Journal

HighTech and Innovation Journal 2024年第1期5卷 16-35页

作者： Sunthornwat, Rapin Sukparungsee, Saowanit Areepong, Yupaporn Industrial Technology and Innovation Management Program Faculty of Science and Technology Pathumwan Institute of Technology 10330 Thailand Department of Applied Statistics Faculty of Applied Science King Mongkut’s University of Technology North Bangkok Bangkok10800 Thailand

This research aims to investigate a Homogenously Weighted Moving Average (HWMA) control chart for detecting minor and moderate shifts in the process mean. A mathematical model for the explicit formulae of the average run length (ARL) of the HWMA control chart based on the autoregressive (AR) process is presented. The efficacy of the HWMA control chart is evaluated based on the average run length, the standard deviation of run length (SDRL), and the median run length (MRL). As illustrations of the design and implementation of the HWMA control chart, numerical examples are provided. In numerous instances, a comparative analysis of the HWMA control chart relative to the Extended Exponentially Weighted Moving Average (Extended EWMA) and cumulative sum (CUSUM) control charts with mean process shifts is performed in detail. Additionally, the relative mean index (RMI), the average extra quadratic loss (AEQL), and the performance comparison index (PCI) are utilized to evaluate the performance of control charts. For various shift sizes, the HWMA control chart is superior to the Extended EWMA and CUSUM control charts. This study applies empirical data from the area of economics to validate the explicit formula of ARL values for the HWMA control chart. © Authors retain all copyrights.

关键词： Control charts

Null Space Properties of Neural Networks with Applications to Image Steganography

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arXiv 2023年

作者： Li, Xiang Short, Kevin M. Integrated Applied Mathematics Program Department of Mathematics and Statistics University of New Hampshire DurhamNH03824 United States

This paper explores the null space properties of neural networks. We extend the null space definition from linear to nonlinear maps and discuss the presence of a null space in neural networks. The null space of a given neural network can tell us the part of the input data that makes no contribution to the final prediction so that we can use it to trick the neural network. This reveals an inherent weakness in neural networks that can be exploited. One application described here leads to a method of image steganography. Through experiments on image datasets such as MNIST, we show that we can use null space components to force the neural network to choose a selected hidden image class, even though the overall image can be made to look like a completely different image. We conclude by showing comparisons between what a human viewer would see, and the part of the image that the neural network is actually using to make predictions and, hence, show that what the neural network "sees" is completely different than what we would expect. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

A Neural Network-Based Approach to Normality Testing for Dependent Data

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arXiv 2023年

作者： Kim, Minwoo Genton, Marc G. Huser, Raphaël Castruccio, Stefano Department of Statistics Pusan National University Korea Republic of Statistics program King Abdullah University of Science and Technology Saudi Arabia Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States

There is a wide availability of methods for testing normality under the assumption of independent and identically distributed data. When data are dependent in space and/or time, however, assessing and testing the marginal behavior is considerably more challenging, as the marginal behavior is impacted by the degree of dependence. We propose a new approach to assess normality for dependent data by non-linearly incorporating existing statistics from normality tests as well as sample moments such as skewness and kurtosis through a neural network. We calibrate (deep) neural networks by simulated normal and non-normal data with a wide range of dependence structures and we determine the probability of rejecting the null hypothesis. We compare several approaches for normality tests and demonstrate the superiority of our method in terms of statistical power through an extensive simulation study. A real world application to global temperature data further demonstrates how the degree of spatio-temporal aggregation affects the marginal normality in the data. © 2023, CC BY.

关键词： Higher order statistics

Spatial Bayesian Neural Networks

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arXiv 2023年

作者： Zammit-Mangion, Andrew Kaminski, Michael D. Tran, Ba-Hien Filippone, Maurizio Cressie, Noel School of Mathematics and Applied Statistics University of Wollongong Australia Paris Research Centre Huawei Technologies France Statistics Program King Abdullah University of Science and Technology Saudi Arabia

Statistical models for spatial processes play a central role in analyses of spatial data. Yet, it is the simple, interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest. Here, we propose a new, flexible class of spatial-process models, which we refer to as spatial Bayesian neural networks (SBNNs). An SBNN leverages the representational capacity of a Bayesian neural network;it is tailored to a spatial setting by incorporating a spatial "embedding layer" into the network and, possibly, spatially-varying network parameters. An SBNN is calibrated by matching its finite-dimensional distribution at locations on a fine gridding of space to that of a target process of interest. That process could be easy to simulate from or we may have many realisations from it. We propose several variants of SBNNs, most of which are able to match the finite-dimensional distribution of the target process at the selected grid better than conventional BNNs of similar complexity. We also show that an SBNN can be used to represent a variety of spatial processes often used in practice, such as Gaussian processes, lognormal processes, and max-stable processes. We briefly discuss the tools that could be used to make inference with SBNNs, and we conclude with a discussion of their advantages and limitations. Copyright © 2023, The Authors. All rights reserved.

关键词： Bayesian networks