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CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

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arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

2D Polynomial Regression Modeling for Predictive Analysis of Glucose Concentration in NP-Model Fractal Microwave Sensor Using Frequency and Transmission Coefficient Disparities

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2D Polynomial Regression Modeling for Predictive Analysis of...

13th International Electrical Engineering Congress, iEECON 2025

作者： Nantapanich, Nutyada Mahatthanajatuphat, Pisit Wongsin, Norakamon Lee, Wilaiporn Rajamangala University of Technology Thanyaburi Faculty of Engineering Department of Electronics and Telecommunication Engineering Pathum Thani Thailand Yothinburana School Regular Program in Mathematics-Science Bangkok Thailand King Mongkut's University of Technology North Bangkok Faculty of Engineering Department of Electrical and Computer Engineering Bangkok Thailand

ISBN: (纸本)9798331543952

The article introduces a two-dimensional polynomial regression model for the predictive analysis of glucose concentration in a fractal microwave sensor NP model, utilizing frequency and transmission coefficient differences to examine their correlation with glucose concentration levels. The sensor employed in this investigation is fabricated on an economical FR-4 substrate to minimize costs. The sensor structure is developed with the fractal structure reduction method established by the NP model to operate at a frequency of roughly 2.97 GHz. The CST Studio software is utilized to analyze the findings from the simulation of the suggested sensor structure. Furthermore, the proposed sensor is integrated into a test apparatus comprising a sensor platform and a liquid tube constructed from PPA material. The liquid under examination is a glucose and water mixture at varying concentrations. It was analyzed using a VNA instrument to evaluate its frequency response and the magnitude of the alteration in the transmission coefficient. The values are utilized to create a two-dimensional polynomial regression model. The experiments demonstrated that the proposed sensor model possesses an Adjusted R² value of 0.99499 and an average error of approximately 3.57% for glucose concentration analysis throughout the range of 5% to 30%, with sensitivities of 0.00879 dB/% for insertion loss and 0.092 MHz/% for frequency variation, facilitating accurate glucose concentration prediction analysis. © 2025 IEEE.

关键词： Polynomial regression

BLIS-Net: Classifying and Analyzing Signals on Graphs

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arXiv 2023年

作者： Xu, Charles Goldman, Laney Guo, Valentina Hollander-Bodie, Benjamin Trank-Greene, Maedee Adelstein, Ian De Brouwer, Edward Ying, Rex Krishnaswamy, Smita Perlmutter, Michael Department of Mathematics Yale University United States Department of Computer Science Yale University United States Department of Mathematics Harvey Mudd College United States Department of Genetics Yale School of Medicine United States Department of Applied Mathematics University of Colorado Boulder United States Department of Mathematics Boise State University United States Program in Computing Boise State University United States

Graph neural networks (GNNs) have emerged as a powerful tool for tasks such as node classification and graph classification. However, much less work has been done on signal classification, where the data consists of many functions (referred to as signals) defined on the vertices of a single graph. These tasks require networks designed differently from those designed for traditional GNN tasks. Indeed, traditional GNNs rely on localized low-pass filters, and signals of interest may have intricate multi-frequency behavior and exhibit long range interactions. This motivates us to introduce the BLIS-Net (Bi-Lipschitz Scattering Net), a novel GNN that builds on the previously introduced geometric scattering transform. Our network is able to capture both local and global signal structure and is able to capture both low-frequency and high-frequency information. We make several crucial changes to the original geometric scattering architecture which we prove increase the ability of our network to capture information about the input signal and show that BLIS-Net achieves superior performance on both synthetic and real-world data sets based on traffic flow and fMRI data. Copyright © 2023, The Authors. All rights reserved.

关键词： Graph neural networks

Dynamic programming Algorithm using Furniture Industry 0/1 Knapsack Problem

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Dynamic Programming Algorithm using Furniture Industry 0/1 K...

International Conference on Cybernetics and Intelligent System (ICORIS)

作者： Mietha Anditta Natashya Amartya Laurens Spits Warnars Harco Leslie Hendric Spits Warnars Arief Ramadhan Teddy Siswanto Teddy Mantoro Nurulhuda Noordin Computer Science Departement School of Computer Science Bina Nusantara University Jakarta Indonesia Information Systems Departement School of Information Systems Bina Nusantara University Jakarta Indonesia Computer Science Departement BINUS Graduate Program - Computer Science Bina Nusantara University Jakarta Indonesia PJJ Informatika Telkom University Bandung Indonesia Information Systems Department Trisakti University Jakarta Indonesia Faculty of Engineering and Technology Sampoerna University Jakarta Indonesia School of Computing Sciences College of Computing Informatics and Mathematics Universiti Teknologi MARA Selangor Malaysia

Dynamic programming is a fundamental algorithm that can be found in our daily lives easily. One of the dynamic programming algorithm implementations consists of solving the 0/1 knapsack problem. A 0/1 knapsack problem can be seen from industrial production cost. It is prevalent that a production cost has to be as efficient as possible, but the expectation is to get the proceeds of the products higher. Thus, the dynamic programming algorithm can be implemented to solve the diverse knapsack problem, one of which is the 0/1 knapsack problem, which would be the main focus of this paper. The implementation was implemented using C language. This paper was created as an early implementation algorithm using a Dynamic program algorithm applied to an Automatic Identification System (AIS) dataset.

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A Deep Learning Approach for Nerve Injury Classification in Brachial Plexopathies Using Magnetic Resonance Neurography with Modified Hiking Optimization Algorithm

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Academic Radiology 2025年

作者： Dahou, Abdelghani Elaziz, Mohamed Abd Khattap, Mohamed G. Hassan, Hend Galal Eldeen Mohamed Ali School of Computer Science and Technology Zhejiang Normal University Jinhua 321004 China Mathematics and Computer Science department University of Ahmed DRAIA Adrar 01000 Algeria Department of Mathematics Faculty of Science Zagazig University Zagazig 44519 Egypt Faculty of Computer Science and Engineering Galala University Suez 435611 Egypt Artificial Intelligence Research Center (AIRC) Ajman University Ajman 346 United Arab Emirates Department of Diagnostic Interventional Radiology and Molecular Imaging Faculty of Medicine Ain Shams University Cairo 11591 Egypt Technology of Radiology and Medical Imaging Program Faculty of Applied Health Sciences Technology Galala University Suez 435611 Egypt

Rationale and Objectives: Brachial plexopathies (BPs) encompass a complex spectrum of nerve injuries affecting motor and sensory function in the upper extremities. Diagnosis is challenging due to the intricate anatomy and symptom overlap with other neuropathies. Magnetic Resonance Neurography (MRN) provides advanced imaging but requires specialized interpretation. This study proposes an AI-based framework that combines deep learning (DL) with the modified Hiking Optimization Algorithm (MHOA) enhanced by a Comprehensive Learning (CL) technique to improve the classification of nerve injuries (neuropraxia, axonotmesis, neurotmesis) using MRN data. Materials and Methods: The framework utilizes MobileNetV4 for feature extraction and MHOA for optimized feature selection across different MRI sequences (STIR, T2, T1, and DWI). A dataset of 39 patients diagnosed with BP was used. The framework classifies injuries based on Seddon's criteria, distinguishing between normal and abnormal conditions as well as injury severity. Results: The model achieved excellent performance, with 1.0000 accuracy in distinguishing normal from abnormal conditions using STIR and T2 sequences. For injury severity classification, accuracy was 0.9820 in STIR, outperforming the original HOA and other metaheuristic algorithms. Additionally, high classification accuracy (0.9667) was observed in DWI. The proposed framework outperformed traditional methods and demonstrated high sensitivity and specificity. Conclusion: The proposed AI-based framework significantly improves the diagnosis of BP by accurately classifying nerve injury types. By integrating DL and optimization techniques, it reduces diagnostic variability, making it a valuable tool for clinical settings with limited specialized neuroimaging expertise. This framework has the potential to enhance clinical decision-making and optimize patient outcomes through precise and timely diagnoses. © 2025 The Association of University Radiologists

关键词： Brachial Plexopathy (BP) Comprehensive Learning (CL) Deep Learning (DL) Feature Selection (FS) Hiking Optimization Algorithm (HOA) Magnetic Resonance Neurography (MRN) MobileNetV4

On Time Uniform Wong-Zakai Approximation Theorems

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arXiv 2023年

作者： Del Moral, Pierre Hu, Shulan Jasra, Ajay Ruzayqat, Hamza Wang, Xinyu Institut de Mathematiques de Bordeaux Bordeaux33405 France School of Statistics and Mathematics Zhongnan University of Economics and Law China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Wenlan School of Business Zhongnan University of Economics and Law China

We consider the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in many areas, such as those with ordinary differential equations associated to random smooth fluctuations;e.g. robust filtering problems. In many examples, the mean error estimate bounds that have been derived in the literature can grow exponentially with respect to the time horizon. We show in a simple example that indeed mean error estimates do explode exponentially in the time parameter, i.e. in that case a Wong-Zakai approximation is only useful for extremely short time intervals. Under spectral conditions, we present some quantitative time-uniform convergence theorems, i.e. time-uniform mean error bounds, yielding what seems to be the first results of this type for Wong-Zakai diffusion *** Codes 60H35(Primary), 65C30(Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Brownian movement

Bounding the sum of the largest signless Laplacian eigenvalues of a graph

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arXiv 2022年

作者： Abiad, Aida de Lima, Leonardo Kalantarzadeh, Sina Mohammadi, Mona Oliveira, Carla Department of Mathematics and Computer Science Eindhoven University of Technology Netherlands Department of Mathematics: Analysis Logic and Discrete Mathematics Ghent University Belgium Department of Mathematics and Data Science Vrije Universiteit Brussel Belgium Graduate Program in Mathematics Federal University of Parana Curitiba Brazil Sharif University of Technology Iran Department of Mathematical National School of Statistical Sciences Rio de Janeiro Brazil

关键词： Eigenvalues and eigenfunctions

Air Quality Prediction Based on Air Pollution Emissions in the City Environment Using XGBoost with SMOTE

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Air Quality Prediction Based on Air Pollution Emissions in t...

International Conference of computer science and Information Technology

作者： Adli A Nababan Sutarman Muhammad Zarlis Erna B Nababan Department of Computer Science Faculty of Computer Science and Information Technology Universitas Sumatera Utara Medan Indonesia Department of Mathematics Faculty of Mathematics and Natural Sciences Universitas Sumatera Utara Medan Indonesia Department of Information Systems Management BINUS Graduate Program-Master of Information Systems Management Bina Nusantara University Jakarta Indonesia

ISBN: (纸本)9798350399080

Air pollution makes it worse in populated regions. Indonesia's major cities are also impacted by air pollution. Due to rising traffic, material consumption by vehicles, industrial growth, land burning, and garbage collection, air quality has altered significantly. Accurate measurement and classification of air quality are required. Results of accurate classification aid in forming governmental regulations. To reach the criteria for livable air quality, we intend to manage controls. Some of the characteristics of air pollution include particulate (PM10) or PM25, sulfides (in the form of SO2), carbon monoxide (CO), ozone (O3), and nitrites (NO2). Using the XGBoost algorithm and synthetic minority oversampling (SMOTE) methods based on the Air Pollution Standard Index (ISPU) category, this study seeks to uncover factors that affect air quality. XGBoost, an ensemble machine learning approach built on a decision tree and applying a gradient reinforcement framework, is the classification algorithm in use. Air quality categorization has been tested and shown to work with the XGBoost algorithm. The dataset used in this study is air quality in 2021 which was collected by the Jakarta Environmental Ministry The proposed classification model will be evaluated using the Repeated k-fold cross-validation method for objective results. The results of the study prove that SMOTE and XGBoost have better performance than using only the XGBoost method in predicting air quality, where the overall accuracy value of SMOTE with XGBoost is 99.60%, The overall precision value is 99.60%, the overall recall value is 99.60% and the overall f1-score is 99.60% and the overall ROC AUC value is 99.96%. The overall SMOTE method with the proposed XGBoost has given better performance in air pollution prediction.

关键词： Machine learning algorithms Urban areas Air pollution Prediction algorithms Particle measurements Regulation Classification algorithms

Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations

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arXiv 2023年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is high-dimensional, but the model for the signal yields longer-range time dependencies through the observation locations. Motivated by this model we revisit a lesser-known and provably convergent computational methodology from [4, 11, 28] that uses sequential Markov Chain Monte Carlo (MCMC) chains. We extend this methodology for data filtering problems with unknown observation locations. We benchmark our algorithms on Linear Gaussian state space models against competing ensemble methods and demonstrate a significant improvement in both execution speed and accuracy. Finally, we implement a realistic case study on a high-dimensional rotating shallow water model (of about 104 - 105 dimensions) with real and synthetic data. The data is provided by the National Oceanic and Atmospheric Administration (NOAA) and contains observations from ocean drifters in a domain of the Atlantic Ocean restricted to the longitude and latitude intervals [-51◦,-41◦], [17◦,27◦] *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2023, CC BY.

关键词： Location